Relevant bibliographies by topics / Computable topology

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Computable topology'

Author: Grafiati
Published: 5 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Computable topology"

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Weihrauch, Klaus, and Tanja Grubba. "Elementary Computable Topology." JUCS - Journal of Universal Computer Science 15, no. (6) (2009): 1381–422. https://doi.org/10.3217/jucs-015-06-1381.

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We revise and extend the foundation of computable topology in the framework of Type-2 theory of effectivity, TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations. We start from a computable topological space, which is a T0-space with a notation of a base such that intersection is computable, and define a number of multi-representations of the points and of the open, the closed and the compact sets and study their properties and relations. We study computability of b
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Weihrauch, Klaus. "Computable Separation in Topology, from T0 to T2." JUCS - Journal of Universal Computer Science 16, no. (18) (2010): 2733–53. https://doi.org/10.3217/jucs-016-18-2733.

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This article continues the study of computable elementary topology started in [Weihrauch and Grubba 2009]. For computable topological spaces we introduce a number of computable versions of the topological separation axioms T0, T1 and T2. The axioms form an implication chain with many equivalences. By counterexamples we show that most of the remaining implications are proper. In particular, it turns out that computable T1 is equivalent to computable T2 and that for spaces without isolated points the hierarchy collapses, that is, the weakest computable T0 axiom WCT0 is equivalent to the stronges
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Brattka, Vasco. "Some Notes on Fine Computability." JUCS - Journal of Universal Computer Science 8, no. (3) (2002): 382–95. https://doi.org/10.3217/jucs-008-03-0382.

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A metric defined by Fine induces a topology on the unit interval which is strictly stronger than the ordinary Euclidean topology and which has some interesting applications in Walsh analysis. We investigate computability properties of a corresponding Fine representation of the real numbers and we construct a structure which characterizes this representation. Moreover, we introduce a general class of Fine computable functions and we compare this class with the class of locally uniformly Fine computable functions defined by Mori. Both classes of functions include all ordinary computable function
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KOROVINA, MARGARITA, and OLEG KUDINOV. "Computable elements and functions in effectively enumerable topological spaces." Mathematical Structures in Computer Science 27, no. 8 (2016): 1466–94. http://dx.doi.org/10.1017/s0960129516000141.

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This paper is a part of the ongoing program of analysing the complexity of various problems in computable analysis in terms of the complexity of the associated index sets. In the framework of effectively enumerable topological spaces, we investigate the following question: given an effectively enumerable topological space whether there exists a computable numbering of all its computable elements. We present a natural sufficient condition on the family of basic neighbourhoods of computable elements that guarantees the existence of a principal computable numbering. We show that weakly-effective
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Lu, Hong, and Klaus Weihrauch. "Computable Riesz Representation for Locally Compact Hausdorff Spaces." JUCS - Journal of Universal Computer Science 14, no. (6) (2008): 845–60. https://doi.org/10.3217/jucs-014-06-0845.

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By the Riesz Representation Theorem for locally compact Hausdorff spaces, for every positive linear functional I on K(X) there is a measure μ such that I(f) =∫ f dμ where K(X) is the set of continuous real functions with compact support on the locally compact Hausdorff space X. In this article we prove a uniformly computable version of this theorem for computably locally compact computable Hausdorff spaces X. We introduce a representation of the positive linear functionals I on K(X) and a representation of the Borel measures on X and prove that for every such functional I a measure μ can be co
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Kalantari, Iraj, and Larry Welch. "On Turing degrees of points in computable topology." MLQ 54, no. 5 (2008): 470–82. http://dx.doi.org/10.1002/malq.200710062.

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Kalantari, Iraj, and Larry Welch. "On degree-preserving homeomorphisms between trees in computable topology." Archive for Mathematical Logic 46, no. 7-8 (2007): 679–93. http://dx.doi.org/10.1007/s00153-007-0056-0.

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SCHRÖDER, MATTHIAS. "The sequential topology on is not regular." Mathematical Structures in Computer Science 19, no. 5 (2009): 943–57. http://dx.doi.org/10.1017/s0960129509990065.

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The compact-open topology on the set of continuous functionals from the Baire space to the natural numbers is well known to be zero-dimensional. We prove that the closely related sequential topology on this set is not even regular. The sequential topology arises naturally as the topology carried by the exponential formed in various cartesian closed categories of topological spaces. Moreover, we give an example of an effectively open subset of that violates regularity. The topological properties of are known to be closely related to an open problem in Computable Analysis. We also show that the
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Brattka, Vasco. "Effective representations of the space of linear bounded operators." Applied General Topology 4, no. 1 (2003): 115. http://dx.doi.org/10.4995/agt.2003.2014.

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<p>Representations of topological spaces by infinite sequences of symbols are used in computable analysis to describe computations in topological spaces with the help of Turing machines. From the computer science point of view such representations can be considered as data structures of topological spaces. Formally, a representation of a topological space is a surjective mapping from Cantor space onto the corresponding space. Typically, one is interested in admissible, i.e. topologically well-behaved representations which are continuous and characterized by a certain maximality condition
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Heath, Philip R. "Two, more readily computable, equivariant Nielsen numbers II." Topology and its Applications 156, no. 2 (2008): 186–204. http://dx.doi.org/10.1016/j.topol.2008.06.007.

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Dissertations / Theses on the topic "Computable topology"

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Olguin, Cl?udio Andr?s Callejas. "A topological and domain theoretical study of total computable functions." PROGRAMA DE P?S-GRADUA??O EM SISTEMAS E COMPUTA??O, 2016. https://repositorio.ufrn.br/jspui/handle/123456789/22327.

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Book chapters on the topic "Computable topology"

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Taylor, Paul. "Foundations for Computable Topology." In The Western Ontario Series in Philosophy of Science. Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-0431-2_14.

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Korovina, Margarita, and Oleg Kudinov. "Computable Topology for Reliable Computations." In Lecture Notes in Computer Science. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-37487-7_15.

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Korovina, Margarita, and Oleg Kudinov. "Outline of Partial Computability in Computable Topology." In Unveiling Dynamics and Complexity. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58741-7_7.

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de Brecht, Matthew. "Some Notes on Spaces of Ideals and Computable Topology." In Lecture Notes in Computer Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-51466-2_3.

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Korovina, Margarita, and Oleg Kudinov. "Highlights of the Rice-Shapiro Theorem in Computable Topology." In Lecture Notes in Computer Science. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74313-4_18.

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Gao, Feng. "On the Role of Computable Error Estimates in the Analysis of Numerical Approximation Algorithms." In From Topology to Computation: Proceedings of the Smalefest. Springer US, 1993. http://dx.doi.org/10.1007/978-1-4612-2740-3_36.

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Stillwell, John. "Recursive Comprehension." In Reverse Mathematics. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691196411.003.0007.

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This chapter proves the equivalences between the weak König lemma and the Heine–Borel, extreme value, and uniform continuity theorems. It also discusses the equivalence of the weak König lemma with two famous theorems of topology: the Brouwer fixed point and the Jordan curve theorems. This latter collection of theorems, lying strictly between RCA<sub>0</sub> and ACA<sub>0</sub>, establishes the importance of the system WKL<sub>0</sub> whose set existence axiom is the weak König lemma. Between them, RCA<sub>0</sub>, WKL<sub>0</sub>, and ACA<sub>0</sub> cover the basic theorems of analysis, and
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Conference papers on the topic "Computable topology"

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Abrahão, Felipe S., Klaus Wehmuth, and Artur Ziviani. "Expected Emergent Algorithmic Creativity and Integration in Dynamic Complex Networks." In III Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2018. http://dx.doi.org/10.5753/etc.2018.3152.

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We present a theoretical investigation of the emergence of complexity or irreducible information in networked computable systems when the network topology may change over time. For this purpose, we build a network model in which nodes are randomly generated Turing machines that obey a communication protocol of imitation of the fittest neighbor. Then, we show that there are topological conditions that trigger a phase transition in which eventually these networked computable systems begin to produce an unlimited amount of bits of expected emergent algorithmic complexity, creativity and integrati
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Meyer, D. G. "A new metric that generates the graph topology and is quite computable." In 29th IEEE Conference on Decision and Control. IEEE, 1990. http://dx.doi.org/10.1109/cdc.1990.203737.

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Kormeier, Thomas, and Stephan Rudolph. "Topological Synthesis of Shell Structures." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99092.

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Currently available tools for classical topology optimization of structures have proven valuable in conceptual design. These tools may provide design direction very early in the design cycle. However, the results subsequently need to be interpreted and translated by an engineer into a consistent CAD-model. This research focuses on the topological design synthesis of shell structures, which is being carried out using a design language approach. The aim of this approach is to automatically generate, modify and optimize an abstract representation of the design. This representation is automaticall
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