Computable Separation in Topology, from T_0 to T_3

Weihrauch, Klaus

doi:10.4230/OASIcs.CCA.2009.2276

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Computable Separation in Topology, from T_0 to T_3

Author Klaus Weihrauch

Part of: Volume: 6th International Conference on Computability and Complexity in Analysis (CCA'09) (CCA 2009)
Part of: Series: Open Access Series in Informatics (OASIcs)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2009-11-25

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OASIcs.CCA.2009.2276.pdf

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DOI: 10.4230/OASIcs.CCA.2009.2276
URN: urn:nbn:de:0030-drops-22764

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Computable topology
computable separation

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Abstract

This article continues the study of computable elementary topology started in (Weihrauch, Grubba 2009). We introduce a number of computable versions of the topological $T_0$ to $T_3$ separation axioms and solve their logical relation completely.  In particular, it turns out that computable $T_1$ is equivalent to computable $T_2$. The strongest axiom $SCT_3$ is used in (Grubba, Schroeder, Weihrauch 2007) to construct a computable metric.

Cite As Get BibTex

Klaus Weihrauch. Computable Separation in Topology, from T_0 to T_3. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 257-268, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009) https://doi.org/10.4230/OASIcs.CCA.2009.2276

Author Details

Klaus Weihrauch

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