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Journal articles on the topic 'Tietze extension theorem'

Author: Grafiati

Published: 24 April 2022

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1

Grabiner, Sandy. "The Tietze Extension Theorem and the Open Mapping Theorem." American Mathematical Monthly 93, no. 3 (March 1986): 190. http://dx.doi.org/10.2307/2323339.

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2

Grabiner, Sandy. "The Tietze Extension Theorem and the Open Mapping Theorem." American Mathematical Monthly 93, no. 3 (March 1986): 190–91. http://dx.doi.org/10.1080/00029890.1986.11971783.

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3

Pąk, Karol. "Tietze Extension Theorem for n-dimensional Spaces." Formalized Mathematics 22, no. 1 (March 30, 2014): 11–19. http://dx.doi.org/10.2478/forma-2014-0002.

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Summary In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic with a convex compact subset of En with a non-empty interior. This article is based on [20]; [23] and [22] can also serve as reference books.

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4

Bakić, Damir. "Tietze extension theorem for Hilbert $C^*$-modules." Proceedings of the American Mathematical Society 133, no. 2 (August 25, 2004): 441–48. http://dx.doi.org/10.1090/s0002-9939-04-07563-x.

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5

Uma, M. K., E. Roja, and G. Balasubramanian. "Tietze extension theorem for pairwise ordered fuzzy extremally disconnected spaces." Mathematica Bohemica 133, no. 4 (2008): 341–49. http://dx.doi.org/10.21136/mb.2008.140624.

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6

Shafer, Paul. "The reverse mathematics of the Tietze extension theorem." Proceedings of the American Mathematical Society 144, no. 12 (June 10, 2016): 5359–70. http://dx.doi.org/10.1090/proc/13217.

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7

Kubiak, Tomasz. "L-fuzzy normal spaces and Tietze extension theorem." Journal of Mathematical Analysis and Applications 125, no. 1 (July 1987): 141–53. http://dx.doi.org/10.1016/0022-247x(87)90169-7.

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8

Kotzé, Wesley, and Tomasz Kubiak. "Insertion of a measurable function." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 57, no. 3 (December 1994): 295–304. http://dx.doi.org/10.1017/s1446788700037708.

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AbstractSome theorems on the existence of continuous real-valued functions on a topological space (for example, insertion, extension, and separation theorems) can be proved without involving uncountable unions of open sets. In particular, it is shown that well-known characterizations of normality (for example the Katětov-Tong insertion theorem, the Tietze extension theorem, Urysohn's lemma) are characterizations of normal σ-rings. Likewise, similar theorems about extremally disconnected spaces are true for σ-rings of a certain type. This σ-ring approach leads to general results on the existence of functions of class α.

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9

Ossa, Erich. "A simple proof of the Tietze-Urysohn extension theorem." Archiv der Mathematik 71, no. 4 (October 1, 1998): 331–32. http://dx.doi.org/10.1007/s000130050272.

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10

Mandelkern, Mark. "A short proof of the Tietze-Urysohn extension theorem." Archiv der Mathematik 60, no. 4 (April 1993): 364–66. http://dx.doi.org/10.1007/bf01207193.

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11

Papageorgiou, Nikolaos S. "On measurable multifunctions with stochastic domain." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 45, no. 2 (October 1988): 204–16. http://dx.doi.org/10.1017/s1446788700030111.

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AbstractIn this paper we prove several random fixed point theorems for multifunctions with a stochastic domain. Then those techniques are used to establish the existence of solutions for random differential inclusions. A useful tool in this process is a stochastic version of the Tietze extension theorems that we prove. Finally we present a stochastic version of the Riesz representation theorem for Hilbert spaces.

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12

BARAN, Tesnim Meryem, and Ayhan ERCİYES. "T4, Urysohn’s lemma, and Tietze extension theorem for constant filter convergence spaces." TURKISH JOURNAL OF MATHEMATICS 45, no. 2 (March 26, 2021): 843–55. http://dx.doi.org/10.3906/mat-2012-101.

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13

Prieto, Carlos. "FLUIDIFICATION OF QUIVERS AND THE TIETZE EXTENSION THEOREM FOR DIAGRAMS OF TOPOLOGICAL SPACES." Quaestiones Mathematicae 11, no. 3 (January 1988): 233–51. http://dx.doi.org/10.1080/16073606.1988.9632142.

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14

FANG, XIAOCHUN. "THE REALIZATION OF MULTIPLIER HILBERT BIMODULE ON BIDUAL SPACE AND TIETZE EXTENSION THEOREM." Chinese Annals of Mathematics 21, no. 03 (July 2000): 375–80. http://dx.doi.org/10.1142/s025295990000039x.

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15

Ahmed, Nasr, Anirudh Pradhan, and F. Salama. "A new topological perspective of expanding space-times with applications to cosmology." International Journal of Geometric Methods in Modern Physics 18, no. 08 (May 12, 2021): 2150130. http://dx.doi.org/10.1142/s0219887821501309.

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We discuss the possible role of the Tietze extension theorem in providing a rigorous topological base to the expanding space-time in cosmology. A simple toy model has been introduced to show the analogy between the topological extension from a circle [Formula: see text] to the whole space [Formula: see text] and the cosmic expansion from a non-zero volume to the whole space-time in non-singular cosmological models. A topological analogy to the cosmic scale factor function has been suggested, the paper refers to the possible applications of the topological extension in mathematical physics.

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16

Degla, Guy Aymard. "Building Infinitely Many Solutions for Some Model of Sublinear Multipoint Boundary Value Problems." Abstract and Applied Analysis 2015 (2015): 1–4. http://dx.doi.org/10.1155/2015/732761.

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We show that the sublinearity hypothesis of some well-known existence results on multipoint Boundary Value Problems (in short BVPs) may allow the existence of infinitely many solutions by using Tietze extension theorem. This is a qualitative result which is of concern in Applied Analysis and can motivate more research on the conditions that ascertain the existence of multiple solutions to sublinear BVPs. The idea of the proof is of independent interest since it shows a constructive way to have ordinary differential equations with multiple solutions.

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17

Giusto, Mariagnese, and Stephen G. Simpson. "Located sets and reverse mathematics." Journal of Symbolic Logic 65, no. 3 (September 2000): 1451–80. http://dx.doi.org/10.2307/2586708.

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AbstractLet X be a compact metric space. A closed set K ⊆ X is located if the distance function d(x, K) exists as a continuous real-valued function on X; weakly located if the predicate d(x, K) > r is allowing parameters. The purpose of this paper is to explore the concepts of located and weakly located subsets of a compact separable metric space in the context of subsystems of second order arithmetic such as RCA0, WKL0 and ACA0. We also give some applications of these concepts by discussing some versions of the Tietze extension theorem. In particular we prove an RCA0 version of this result for weakly located closed sets.

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18

Brown, Lawrence G. "Close hereditary C*-subalgebras and the structure of quasi-multipliers." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 2 (January 16, 2017): 263–92. http://dx.doi.org/10.1017/s0308210516000172.

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We answer a question of Takesaki by showing that the following can be derived from the thesis of Shen: if A and B are σ-unital hereditary C*-subalgebras of C such that ‖p – q‖ < 1, where p and q are the corresponding open projections, then A and B are isomorphic. We give some further elaborations and counterexamples with regard to the σ-unitality hypothesis. We produce a natural one-to-one correspondence between complete order isomorphisms of C*-algebras and invertible left multipliers of imprimitivity bimodules. A corollary of the above two results is that any complete order isomorphism between σ-unital C*-algebras is the composite of an isomorphism with an inner complete order isomorphism. We give a separable counterexample to a question of Akemann and Pedersen; namely, the space of quasi-multipliers is not linearly generated by left and right multipliers. But we show that the space of quasi-multipliers is multiplicatively generated by left and right multipliers in the σ-unital case. In particular, every positive quasi-multiplier is of the form T*T for T a left multiplier. We show that a Lie theory consequence of the negative result just stated is that the map sending T to T*T need not be open, even for very nice C*-algebras. We show that surjective maps between σ-unital C*-algebras induce surjective maps on left, right, and quasi-multipliers. (The more significant similar result for multipliers is Pedersen's non-commutative Tietze extension theorem.) We elaborate the relations of the above with continuous fields of Hilbert spaces and in so doing answer a question of Dixmier and Douady. We discuss the relationship of our results to the theory of perturbations of C*-algebras.

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19

Bartelt, Martin W., and John J. Swetits. "An Elementary Extension of Tietze's Theorem." Mathematics Magazine 66, no. 5 (December 1, 1993): 330. http://dx.doi.org/10.2307/2690518.

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20

Bartelt, Martin W., and John J. Swetits. "An Elementary Extension of Tietze's Theorem." Mathematics Magazine 66, no. 5 (December 1993): 330–32. http://dx.doi.org/10.1080/0025570x.1993.11996162.

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21

Narici, Lawrence, and Edward Beckenstein. "On Continuous Extensions." gmj 3, no. 6 (December 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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22

Reagor, Mary P., and David F. Addis. "Tietze's extension theorem in fuzzy topological spaces." Fuzzy Sets and Systems 30, no. 3 (May 1989): 297–313. http://dx.doi.org/10.1016/0165-0114(89)90021-3.

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23

Hernández-Muñoz, Salvador. "Approximation and extension of continuous functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 57, no. 2 (October 1994): 149–57. http://dx.doi.org/10.1017/s1446788700037484.

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AbstractIn this paper we study the approximation of vector valued continuous functions defined on a topological space and we apply this study to different problems. Thus we give a new proof of Machado's Theorem. Also we get a short proof of a Theorem of Katětov and we prove a generalization of Tietze's Extension Theorem for vector-valued continuous functions, thereby solving a question left open by Blair.

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24

CÎRSTEA, FLORICA C. "PROOFS OF URYSOHN’S LEMMA AND THE TIETZE EXTENSION THEOREM VIA THE CANTOR FUNCTION." Bulletin of the Australian Mathematical Society, July 3, 2020, 1–7. http://dx.doi.org/10.1017/s000497272000057x.

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Urysohn’s lemma is a crucial property of normal spaces that deals with separation of closed sets by continuous functions. It is also a fundamental ingredient in proving the Tietze extension theorem, another property of normal spaces that deals with the existence of extensions of continuous functions. Using the Cantor function, we give alternative proofs for Urysohn’s lemma and the Tietze extension theorem.

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25

ROJA, E., M. K. UMA, and G. BALASUBRAMANIAN. "ORDERED L-FUZZY Gd-EXTREMALLY DISCONNECTED SPACES AND TIETZE EXTENSION THEOREM." Proyecciones (Antofagasta) 27, no. 3 (December 2008). http://dx.doi.org/10.4067/s0716-09172008000300002.

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26

Aschenbrenner, Matthias, and Athipat Thamrongthanyalak. "Michael’s Selection Theorem in a semilinear context." Advances in Geometry 15, no. 3 (January 1, 2015). http://dx.doi.org/10.1515/advgeom-2015-0018.

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