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Journal articles on the topic 'Space Of Continuous Functions'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

ALIPRANTIS, CHARALAMBOS D., DAVID HARRIS, and RABEE TOURKY. "CONTINUOUS PIECEWISE LINEAR FUNCTIONS." Macroeconomic Dynamics 10, no. 1 (2005): 77–99. http://dx.doi.org/10.1017/s1365100506050103.

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The paper studies the function space of continuous piecewise linear functions in the space of continuous functions on them-dimensional Euclidean space. It also studies the special case of one dimensional continuous piecewise linear functions. The study is based on the theory of Riesz spaces that has many applications in economics. The work also provides the mathematical background to its sister paper Aliprantis, Harris, and Tourky (2006), in which we estimate multivariate continuous piecewise linear regressions by means of Riesz estimators, that is, by estimators of the the Boolean formwhereX=

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2

Abdullah, Laila S., and Diyar M. Mohammed. "On almost and weakly ip -continuous functions in topological space." Journal of Zankoy Sulaimani - Part A 18, no. 2 (2016): 259–72. http://dx.doi.org/10.17656/jzs.10520.

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3

Beer, Gerald. "More about metric spaces on which continuous functions are uniformly continuous." Bulletin of the Australian Mathematical Society 33, no. 3 (1986): 397–406. http://dx.doi.org/10.1017/s0004972700003981.

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An Atsuji space is a metric space X such that each continuous function form X to an arbitrary metric space Y is uniformly continuous. We here present (i) characterizations of metric spaces with Atsuji completions; (ii) Cantor-type theorems for Atsuji spaces; (iii) a fixed point theorem for self-maps of an Atsuji space.

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4

Al-Nashef, Bassam. "rc-continuous functions and functions with rc-strongly closed graph." International Journal of Mathematics and Mathematical Sciences 2003, no. 72 (2003): 4547–55. http://dx.doi.org/10.1155/s0161171203203410.

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The family of regular closed subsets of a topological space is used to introduce two concepts concerning a functionffrom a spaceXto a spaceY. The first of them is the notion offbeing rc-continuous. One of the established results states that a spaceYis extremally disconnected if and only if each continuous function from a spaceXtoYis rc-continuous. The second concept studied is the notion of a functionfhaving an rc-strongly closed graph. Also one of the established results characterizes rc-compact spaces (≡S-closed spaces) in terms of functions that possess rc-strongly closed graph.

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5

Dow, Alan, та Petr Simon. "Spaces of continuous functions over a Ψ-space". Topology and its Applications 153, № 13 (2006): 2260–71. http://dx.doi.org/10.1016/j.topol.2005.02.013.

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6

Mykhaylyuk, V. V. "Lebesgue Measurability of Separately Continuous Functions and Separability." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–4. http://dx.doi.org/10.1155/2007/54159.

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A connection between the separability and the countable chain condition of spaces withL-property (a topological spaceXhasL-property if for every topological spaceY, separately continuous functionf:X×Y→ℝand open setI⊆ℝ,the setf−1(I)is anFσ-set) is studied. We show that every completely regular Baire space with theL-property and the countable chain condition is separable and constructs a nonseparable completely regular space with theL-property and the countable chain condition. This gives a negative answer to a question of M. Burke.

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7

Llavona, J. G., and J. A. Jaramillo. "Homomorphisms Between Algebras of Continuous Functions." Canadian Journal of Mathematics 41, no. 1 (1989): 132–62. http://dx.doi.org/10.4153/cjm-1989-007-8.

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We are concerned in this paper with the study of homomorphisms between different algebras of continuous functions, especially the algebras of real functions which are either weakly continuous on bounded sets or weakly uniformly continuous on bounded sets on a Banach space (see definitions below).These spaces of weakly [uniformly] continuous functions appeared in relation with some questions in Infinite-dimensional Approximation Theory (see [4], [6], [11], [12], [13] and [16]); and since the structure of these function spaces is closely related with properties of different weak topologies (the

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8

Ciesielski, K., and L. Larson. "The space of density continuous functions." Acta Mathematica Hungarica 58, no. 3-4 (1991): 289–96. http://dx.doi.org/10.1007/bf01903959.

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9

Kawai, Tatsuji. "Formally continuous functions on Baire space." Mathematical Logic Quarterly 64, no. 3 (2018): 192–200. http://dx.doi.org/10.1002/malq.201700015.

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10

HATORI, OSAMU. "SEPARATION PROPERTIES AND OPERATING FUNCTIONS ON A SPACE OF CONTINUOUS FUNCTIONS." International Journal of Mathematics 04, no. 04 (1993): 551–600. http://dx.doi.org/10.1142/s0129167x93000303.

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Characterizations of the space CR (X) of all real-valued continuous functions on a compact Hausdorff space X among its subspaces are investigated under the circumstances of operating functions. One of the main purpose in this paper is to disprove the following conjecture: if a non-affine function operates on an ultraseparating real Banach function space E on X, then E = CR (X). A positive answer is given in the case that E satisfies a stronger separation axiom than ultraseparation one, which the real part of an ultraseparating Banach function algebra satisfies. For the original conjecture a co

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11

Voloshyn, H. A., and V. K. Maslyuchenko. "Sequential Closure of the Space of Jointly Continuous Functions in the Space of Separately Continuous Functions." Ukrainian Mathematical Journal 68, no. 2 (2016): 171–78. http://dx.doi.org/10.1007/s11253-016-1216-3.

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12

Grushka, Yaroslav I. "On monotonous separately continuous functions." Applied General Topology 20, no. 1 (2019): 75. http://dx.doi.org/10.4995/agt.2019.9817.

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<p>Let T = (<strong>T</strong>, ≤) and T<sub>1</sub>= (<strong>T</strong><sub>1</sub> , ≤<sub>1</sub>) be linearly ordered sets and X be a topological space. The main result of the paper is the following: If function ƒ(t,x) : <strong>T</strong> × X → <strong>T</strong><sub>1 </sub>is continuous in each variable (“t” and “x”) separately and function ƒ<sub>x</sub>(t) = ƒ(t,x) is monotonous on <strong>T</strong> for every x ∈ X, then ƒ is continuous mapping from<strong&

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13

Fleischer, Isidore. ""Place Functions": Alias Continuous Functions on the Stone Space." Proceedings of the American Mathematical Society 106, no. 2 (1989): 451. http://dx.doi.org/10.2307/2048826.

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14

Fleischer, I. "‘‘Place functions”: alias continuous functions on the Stone space." Proceedings of the American Mathematical Society 106, no. 2 (1989): 451. http://dx.doi.org/10.1090/s0002-9939-1989-0967485-9.

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15

Nakaoka, Fumie, and Nobuyuki Oda. "Continuous functions between sets with operations." Acta et Commentationes Universitatis Tartuensis de Mathematica 24, no. 2 (2020): 225–39. http://dx.doi.org/10.12697/acutm.2020.24.15.

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A set with an operation is a generalization of a topological space. Two types of continuous functions are dened between sets with operations. They are characterized making use of two types of closures and interiors. Homeomorphisms between sets with operations are also characterized. Variants of subspaces, connected spaces and compact spaces are introduced in a set with an operation and some fundamental properties of them are proved.

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16

Banakh, Taras, Małgorzata Filipczak, and Julia Wódka. "Returning functions with closed graph are continuous." Mathematica Slovaca 70, no. 2 (2020): 297–304. http://dx.doi.org/10.1515/ms-2017-0352.

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Abstract A function f : X → ℝ defined on a topological space X is called returning if for any point x ∈ X there exists a positive real number Mx such that for every path-connected subset Cx ⊂ X containing the point x and any y ∈ Cx ∖ {x} there exists a point z ∈ Cx ∖ {x, y} such that |f(z)| ≤ max{Mx, |f(y)|}. A topological space X is called path-inductive if a subset U ⊂ X is open if and only if for any path γ : [0, 1] → X the preimage γ–1(U) is open in [0, 1]. The class of path-inductive spaces includes all first-countable locally path-connected spaces and all sequential locally contractible

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17

Noiri, Takashi. "Weaklyα-continuous functions". International Journal of Mathematics and Mathematical Sciences 10, № 3 (1987): 483–90. http://dx.doi.org/10.1155/s0161171287000565.

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In this paper, we introduce the notion of weaklyα-continuous functions in topological spaces. Weakα-continuity and subweak continuity due to Rose [1] are independent of each other and are implied by weak continuity due to Levine [2]. It is shown that weaklyα-continuous surjections preserve connected spaces and that weaklyα-continuous functions into regular spaces are continuous. Corollary1of [3] and Corollary2of [4] are improved as follows: Iff1:X→Yis a semi continuous function into a Hausdorff spaceY,f2:X→Yis either weaklyα-continuous or subweakly continuous, andf1=f2on a dense subset ofX, th

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18

Yamazaki, Hiroshi, Keiichi Miyajima, and Yasunari Shidama. "Functional Space Consisted by Continuous Functions on Topological Space." Formalized Mathematics 29, no. 1 (2021): 49–62. http://dx.doi.org/10.2478/forma-2021-0005.

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Summary In this article, using the Mizar system [1], [2], first we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space [5]. We prove that this functional space is a Banach space [3]. Next, we give a definition of a function space which is constructed from all continuous functions with bounded support. We also prove that this function space is a normed space.

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19

Dontchev, J. "Contra-continuous functions and stronglyS-closed spaces." International Journal of Mathematics and Mathematical Sciences 19, no. 2 (1996): 303–10. http://dx.doi.org/10.1155/s0161171296000427.

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In 1989 Ganster and Reilly [6] introduced and studied the notion ofLC-continuous functions via the concept of locally closed sets. In this paper we consider a stronger form ofLC-continuity called contra-continuity. We call a functionf:(X,τ)→(Y,σ)contra-continuous if the preimage of every open set is closed. A space(X,τ)is called stronglyS-closed if it has a finite dense subset or equivalently if every cover of(X,τ)by closed sets has a finite subcover. We prove that contra-continuous images of stronglyS-closed spaces are compact as well as that contra-continuous,β-continuous images ofS-closed s

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20

Viswanathan, P., and M. A. Navascués. "A Fractal Operator on Some Standard Spaces of Functions." Proceedings of the Edinburgh Mathematical Society 60, no. 3 (2017): 771–86. http://dx.doi.org/10.1017/s0013091516000316.

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AbstractThrough appropriate choices of elements in the underlying iterated function system, the methodology of fractal interpolation enables us to associate a family of continuous self-referential functions with a prescribed real-valued continuous function on a real compact interval. This procedure elicits what is referred to as anα-fractal operator on, the space of all real-valued continuous functions defined on a compact intervalI. With an eye towards connecting fractal functions with other branches of mathematics, in this paper we continue to investigate the fractal operator in more general

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21

Cambern, Michael, and Peter Greim. "Spaces of Continuous Vector Functions as Duals." Canadian Mathematical Bulletin 31, no. 1 (1988): 70–78. http://dx.doi.org/10.4153/cmb-1988-011-3.

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AbstractA well known result due to Dixmier and Grothendieck for spaces of continuous scalar-valued functions C(X), X compact Hausdorff, is that C(X) is a Banach dual if, and only if, Xis hyperstonean. Moreover, for hyperstonean X, the predual of C(X) is strongly unique. Here we obtain a formulation of this result for spaces of continuous vector-valued functions. It is shown that if E is a Hilbert space and C(X, (E, σ *) ) denotes the space of continuous functions on X to E when E is provided with its weak * ( = weak) topology, then C(X, (E, σ *) ) is a Banach dual if, and only if, X is hyperst

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22

Bastin, Françoise. "Distinguishedness of weighted Fréchet spaces of continuous functions." Proceedings of the Edinburgh Mathematical Society 35, no. 2 (1992): 271–83. http://dx.doi.org/10.1017/s0013091500005538.

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In this paper, we prove that if is an increasing sequence of strictly positive and continuous functions on a locally compact Hausdorff space X such that then the Fréchet space C(X) is distinguished if and only if it satisfies Heinrich's density condition, or equivalently, if and only if the sequence satisfies condition (H) (cf. e.g.‵[1] for the introduction of (H)). As a consequence, the bidual λ∞(A) of the distinguished Köthe echelon space λ0(A) is distinguished if and only if the space λ1(A) is distinguished. This gives counterexamples to a problem of Grothendieck in the context of Köthe ech

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23

Di Maio, G., L' Holá, D. Holý, and R. A. McCoy. "Topologies on the space of continuous functions." Topology and its Applications 86, no. 2 (1998): 105–22. http://dx.doi.org/10.1016/s0166-8641(97)00114-4.

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24

Bagchi, S. C., and B. V. Rao. "Continuous functions on the space of probabilities." Proceedings of the American Mathematical Society 95, no. 3 (1985): 474. http://dx.doi.org/10.1090/s0002-9939-1985-0806090-8.

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25

Latif, Raja Mohammad. "Delta – Open Sets And Delta – Continuous Functions." International Journal of Pure Mathematics 8 (February 9, 2021): 1–22. http://dx.doi.org/10.46300/91019.2021.8.1.

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In 1968 Velicko [30] introduced the concepts of δ-closure and δ-interior operations. We introduce and study properties of δ-derived, δ-border, δ-frontier and δ-exterior of a set using the concept of δ-open sets. We also introduce some new classes of topological spaces in terms of the concept of δ-D- sets and investigate some of their fundamental properties. Moreover, we investigate and study some further properties of the well-known notions of δ-closure and δ-interior of a set in a topological space. We also introduce δ-R0 space and study its characteristics. We also introduce δ-R0 space and s

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26

Heikkinen, Toni, Juha Lehrbäck, Juho Nuutinen, and Heli Tuominen. "Fractional Maximal Functions in Metric Measure Spaces." Analysis and Geometry in Metric Spaces 1 (May 28, 2013): 147–62. http://dx.doi.org/10.2478/agms-2013-0002.

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Abstract We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.

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27

Aron, R. M., B. J. Cole, and T. W. Gamelin. "Weak-Star Continuous Analytic Functions." Canadian Journal of Mathematics 47, no. 4 (1995): 673–83. http://dx.doi.org/10.4153/cjm-1995-035-1.

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AbstractLet 𝒳 be a complex Banach space, with open unit ball B. We consider the algebra of analytic functions on B that are weakly continuous and that are uniformly continuous with respect to the norm. We show these are precisely the analytic functions on B that extend to be weak-star continuous on the closed unit ball of 𝒳**. If 𝒳* has the approximation property, then any such function is approximable uniformly on B by finite polynomials in elements of 𝒳*. On the other hand, there exist Banach spaces for which these finite-type polynomials fail to approximate. We consider also the approximati

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28

Sidorenko, N. G. "Nonisomorphy of certain Banach spaces of smooth functions to the space of continuous functions." Functional Analysis and Its Applications 21, no. 4 (1988): 340–42. http://dx.doi.org/10.1007/bf01077817.

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29

Celeghini, Enrico, Manuel Gadella, and Mariano A. del Olmo. "Groups, Special Functions and Rigged Hilbert Spaces." Axioms 8, no. 3 (2019): 89. http://dx.doi.org/10.3390/axioms8030089.

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We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions serve as bases for infinite dimensional Hilbert spaces supporting linear unitary irreducible representations of a given Lie group. These representations are explicitly given by operators on the Hilbert space H and the generators of the Lie algebra are represented by unbounded self-adjoint operators. The action of these operators on elements of contin

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30

Cambern, Michael. "A Banach–Stone theorem for spaces of weak* continuous functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 101, no. 3-4 (1985): 203–6. http://dx.doi.org/10.1017/s0308210500020771.

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SynopsisIf X is a compact Hausdorff space and E a dual Banach space, let C(X, Eσ*) denote the Banach space of continuous functions F from X to E when the latter space is provided with its weak * topology, normed by . It is shown that if X and Y are extremally disconnected compact Hausdorff spaces and E is a uniformly convex Banach space, then the existence of an isometry between C(X, Eσ*) and C(Y, Eσ*) implies that X and Y are homeomorphic.

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31

Ganster, M., and I. L. Reilly. "Locally closed sets andLC-continuous functions." International Journal of Mathematics and Mathematical Sciences 12, no. 3 (1989): 417–24. http://dx.doi.org/10.1155/s0161171289000505.

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In this paper we introduce and study three different notions of generalized continuity, namely LC-irresoluteness, LC-continuity and sub-LC-continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a topological space X is locally closed if it is the intersection of an open and a closed set. We discuss some properties of these functions and show that a function between topological spaces is continuous if and only if it is sub-LC-continuous and nearly continuous in the sense of Ptak. Several examples are provided to illustrate the behavior of these new

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32

Render, Herman, and Lothar Rogge. "Pointwise measurable functions." MATHEMATICA SCANDINAVICA 95, no. 2 (2004): 305. http://dx.doi.org/10.7146/math.scand.a-14462.

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We introduce the new concept of pointwise measurability. It is shown in this paper that a measurable function is measurable at each point and that for a large class of topological spaces the converse also holds. Moreover it can be seen that a function which is continuous at a point is Borel-measurable at this point too. Furthermore the set of measurability points is considered. If the range space is a $\sigma$-compact metric space, then this set is a $G_{\delta}$-set; if the range space is only a Polish space this is in general not true any longer.

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Matoušková, Eva. "Extensions of Continuous and Lipschitz Functions." Canadian Mathematical Bulletin 43, no. 2 (2000): 208–17. http://dx.doi.org/10.4153/cmb-2000-028-0.

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AbstractWe show a result slightly more general than the following. Let K be a compact Hausdorff space, F a closed subset of K, and d a lower semi-continuous metric on K. Then each continuous function ƒ on F which is Lipschitz in d admits a continuous extension on K which is Lipschitz in d. The extension has the same supremum norm and the same Lipschitz constant.As a corollary we get that a Banach space X is reflexive if and only if each bounded, weakly continuous and norm Lipschitz function defined on a weakly closed subset of X admits a weakly continuous, norm Lipschitz extension defined on t

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34

Sharp, Bernice. "The differentiability of convex functions on topological linear spaces." Bulletin of the Australian Mathematical Society 42, no. 2 (1990): 201–13. http://dx.doi.org/10.1017/s0004972700028379.

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In this paper topological linear spaces are categorised according to the differentiability properties of their continuous convex functions. Mazur's Theorem for Banach spaces is generalised: all separable Baire topological linear spaces are weak Asplund. A class of spaces is given for which Gateaux and Fréchet differentiability of a continuous convex function coincide, which with Mazur's theorem, implies that all Montel Fréchet spaces are Asplund spaces. The effect of weakening the topology of a given space is studied in terms of the space's classification. Any topological linear space with its

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35

Afrooz, Susan, Fariborz Azarpanah, and Masoomeh Etebar. "On rings of real valued clopen continuous functions." Applied General Topology 19, no. 2 (2018): 203. http://dx.doi.org/10.4995/agt.2018.7667.

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<p>Among variant kinds of strong continuity in the literature, the clopen continuity or cl-supercontinuity (i.e., inverse image of every open set is a union of clopen sets) is considered in this paper. We investigate and study the ring C<sub>s</sub>(X) of all real valued clopen continuous functions on a topological space X. It is shown that every ƒ ∈ C<sub>s</sub>(X) is constant on each quasi-component in X and using this fact we show that C<sub>s</sub>(X) ≅ C(Y), where Y is a zero-dimensional s-quotient space of X. Whenever X is locally connected, we

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36

QUAS, ANTHONY, and JASON SIEFKEN. "Ergodic optimization of super-continuous functions on shift spaces." Ergodic Theory and Dynamical Systems 32, no. 6 (2011): 2071–82. http://dx.doi.org/10.1017/s0143385711000629.

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AbstractErgodic optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that ‘most’ functions are optimized by measures supported on a periodic orbit, and it has been proved in several separable spaces that an open and dense subset of functions is optimized by measures supported on a periodic orbit. All known positive results have been for separable spaces. We give in this paper the first positive result for a non-separable space, the space of super-continuous functions on the full shift, where the set of fun

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37

Camerlo, Riccardo. "Continuous reducibility: functions versus relations." Reports on Mathematical Logic 54 (2019): 45–63. http://dx.doi.org/10.4467/20842589rm.19.002.10650.

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It is proved that the Tang-Pequignot reducibility (or reducibility by relatively continuous relations) on a second countable, T0 space X either coincides with the Wadge reducibility for the given topology, or there is no topology on X that can turn it into Wadge reducibility.

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Saab, Paulette, and Brenda Smith. "Nuclear operators on spaces of continuous vector-valued functions." Glasgow Mathematical Journal 33, no. 2 (1991): 223–30. http://dx.doi.org/10.1017/s0017089500008259.

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Let Ω: be a compact Hausdorff space, let E be a Banach space, and let C(Ω, E) stand for the Banach space of continuous E-valued functions on Ω under supnorm. It is well known [3, p. 182] that if F is a Banach space then any bounded linear operator T:C(Ω, E)→ F has a finitely additive vector measure G defined on the σ-field of Borel subsets of Ω with values in the space ℒ(E, F**) of bounded linear operators from E to the second dual F** of F. The measure G is said to represent T. The purpose of this note is to study the interplay between certain properties of the operator T and properties of th

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Meena, K., and K. Sivakamasundari. "∆*-Locally Continuous Functions and ∆*-Locally Irresolute Maps in Topological Spaces." International Journal of Engineering & Technology 7, no. 4.10 (2018): 407. http://dx.doi.org/10.14419/ijet.v7i4.10.21027.

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The objective of the paper is to introduce a new types of continuous maps and irresolute functions called ∆*-locally continuous functions and ∆*-irresolute maps in topological spaces. The comparative study between these functions with other existing maps is discussed in this paper. Some significant results are also proved as an application of new spaces namely, ∆*-submaximal space and –space. Further the characteristics of these maps under composition maps are exhibited.

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40

Carroy, Raphaël. "A quasi-order on continuous functions." Journal of Symbolic Logic 78, no. 2 (2013): 633–48. http://dx.doi.org/10.2178/jsl.7802150.

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AbstractWe define a quasi-order on Borel functions from a zero-dimensional Polish space into another that both refines the order induced by the Baire hierarchy of functions and generalises the embeddability order on Borel sets. We study the properties of this quasi-order on continuous functions, and we prove that the closed subsets of a zero-dimensional Polish space are well-quasi-ordered by bi-continuous embeddability.

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Jin, Ying-Ying, Li-Hong Xie, and Hong-Wei Yue. "Monotone insertion of semi-continuous functions on stratifiable spaces." Filomat 31, no. 3 (2017): 575–84. http://dx.doi.org/10.2298/fil1703575j.

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In this paper, we consider the problem of inserting semi-continuous function above the (generalized) real-valued function in a monotone fashion. We provide some characterizations of stratifiable spaces, semi-stratifiable spaces, and k-monotonically countably metacompact spaces (k-MCM) and so on. It is established that: (1) A space X is k-MCM if and only if for each locally bounded real-valued function h : X ? R, there exists a lower semi-continuous and k-upper semi-continuous function h': X ? R such that (i) |h|? h', (ii) h'1 ? h'2 whenever |h1| ? |h2|. (2) A space X is stratifiable if and onl

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42

Bednov, B. B. "Steiner points in the space of continuous functions." Moscow University Mathematics Bulletin 66, no. 6 (2011): 255–59. http://dx.doi.org/10.3103/s0027132211060064.

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Amer Kamel, Rehab, and Mayada Ali Kareem. "On the n-Normed Space of Continuous Functions." Journal of Engineering and Applied Sciences 14, no. 22 (2019): 8312–14. http://dx.doi.org/10.36478/jeasci.2019.8312.8314.

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44

Rippon, P. J. "Asymptotic values of continuous functions in Euclidean space." Mathematical Proceedings of the Cambridge Philosophical Society 111, no. 2 (1992): 309–18. http://dx.doi.org/10.1017/s030500410007540x.

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45

Górka, Przemysław. "Maximal operator on the space of continuous functions." Annales Fennici Mathematici 46, no. 1 (2021): 523–26. http://dx.doi.org/10.5186/aasfm.2021.4633.

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V. Marigoudar, Tippeshi, and Imtiyaz M. Teredhahalli. "Some Studies of spgTc space & Continuous Functions." International Journal of Mathematics Trends and Technology 67, no. 6 (2021): 195–97. http://dx.doi.org/10.14445/22315373/ijmtt-v67i6p521.

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Kocinac, Ljubisa. "On spaces of group-valued functions." Filomat 25, no. 2 (2011): 163–72. http://dx.doi.org/10.2298/fil1102163k.

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Narici, Lawrence, and Edward Beckenstein. "On Continuous Extensions." gmj 3, no. 6 (1996): 565–70. http://dx.doi.org/10.1515/gmj.1996.565.

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Abstract We consider various possibilities concerning the continuous extension of continuous functions taking values in an ultrametric space. In Section 1 we consider Tietze-type extension theorems concerning continuous extendibility of continuous functions from compact and closed subsets to the whole space. In Sections 2 and 3 we consider extending “separated” continuous functions in such a way that certain continuous extensions remain separated. Functions taking values in a complete ultravalued field are dealt with in Section 2, and the real and complex cases in Section 3.

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Khan, Liaqat Ali. "On approximation in weighted spaces of continuous vector-valued functions." Glasgow Mathematical Journal 29, no. 1 (1987): 65–68. http://dx.doi.org/10.1017/s0017089500006662.

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The fundamental work on approximation in weighted spaces of continuous functions on a completely regular space has been done mainly by Nachbin ([5], [6]). Further investigations have been made by Summers [10], Prolla ([7], [8]), and other authors (see the monograph [8] for more references). These authors considered functions with range contained in the scalar field or a locally convex topological vector space. In the present paper we prove some approximation results without local convexity of the range space.

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Singh, R. K., and Jasbir Singh Manhas. "Multiplication operators on weighted spaces of vector-valued continuous functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 50, no. 1 (1991): 98–107. http://dx.doi.org/10.1017/s1446788700032584.

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AbstractIf V is a system of weights on a completely regular Hausdorff space X and E is alocally convex space, then CV0(X, E) and CVb (X, E) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.

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