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Reversible spaces and products
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Nipissing University, Ontario, Canada.
2017 (English)In: Topology Proceedings, ISSN 0146-4124, E-ISSN 2331-1290, Vol. 49, p. 317-320Article in journal (Refereed) Published
Abstract [en]

A topological space is reversible if every continuous bijection f:X→X is a homeomorphism. There are many examples of reversiblespaces; in particular, Hausdorff compact spaces and locally Euclidean spaces are such. Chatyrko and Hattori observed, in a manuscript, that any product of topological spaces is non-reversible whenever at least one of the spaces is non-reversible and asked whether the topological product of two connected reversible spaces is reversible. The authors prove here that there are connected reversible spaces such that their product is not reversible. In fact, they construct a reversible space X which is a connected 2-manifold in R3 without boundary such that X×[0,1] is not reversible.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2017. Vol. 49, p. 317-320
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-152294OAI: oai:DiVA.org:liu-152294DiVA, id: diva2:1259242
Available from: 2018-10-29 Created: 2018-10-29 Last updated: 2018-11-09Bibliographically approved

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Chatyrko, Vitalij

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