Fixed points arising only in the growth of first countable spaces
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- by Stephen Watson
- Proc. Amer. Math. Soc. 122 (1994), 613-617
- DOI: https://doi.org/10.1090/S0002-9939-1994-1284460-X
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Abstract:
We construct a Tychonoff first countable space X and an autohomeomorphism f with no fixed points (either a translation or a reflection) such that $\beta f$ does have a fixed point answering a question of Krawczyk and Steprāns. We do this by replacing each point of Mrowka’s construction of a first countable space whose growth has size one with a copy of the integers which can be translated.References
- Aleksander Błaszczyk and Dok Yong Kim, A topological version of a combinatorial theorem of Katětov, Comment. Math. Univ. Carolin. 29 (1988), no. 4, 657–663. MR 982783
- Eric K. van Douwen, $\beta X$ and fixed-point free maps, Topology Appl. 51 (1993), no. 2, 191–195. MR 1229715, DOI 10.1016/0166-8641(93)90152-4
- Eric K. van Douwen, Hausdorff gaps and a nice countably paracompact nonnormal space, Topology Proceedings, Vol. I (Conf., Auburn Univ., Auburn, Ala., 1976) Math. Dept., Auburn Univ., Auburn, Ala., 1977, pp. 239–242. MR 0454915
- Adam Krawczyk and J. Steprāns, Continuous colourings of closed graphs, Topology Appl. 51 (1993), no. 1, 13–26. MR 1229497, DOI 10.1016/0166-8641(93)90011-2 K. Mazur, Rationals and irrationals, unpublished note.
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 613-617
- MSC: Primary 54D35; Secondary 54C20, 54H25
- DOI: https://doi.org/10.1090/S0002-9939-1994-1284460-X
- MathSciNet review: 1284460