OASIcs.CCA.2009.2276.pdf
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Computable Separation in Topology, from T_0 to T_3
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6th International Conference on Computability and Complexity in Analysis (CCA'09) (CCA 2009)
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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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
https://doi.org/10.4230/OASIcs.CCA.2009.2276
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.
Keywords
- Computable topology
- computable separation
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