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.
@InProceedings{weihrauch:OASIcs.CCA.2009.2276, author = {Weihrauch, Klaus}, title = {{Computable Separation in Topology, from T\underline0 to T\underline3}}, booktitle = {6th International Conference on Computability and Complexity in Analysis (CCA'09)}, pages = {257--268}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-939897-12-5}, ISSN = {2190-6807}, year = {2009}, volume = {11}, editor = {Bauer, Andrej and Hertling, Peter and Ko, Ker-I}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2276}, URN = {urn:nbn:de:0030-drops-22764}, doi = {10.4230/OASIcs.CCA.2009.2276}, annote = {Keywords: Computable topology, computable separation} }
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