On the homotopy type of irregular sets
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- by P. F. Duvall and L. S. Husch PDF
- Proc. Amer. Math. Soc. 38 (1973), 419-422 Request permission
Abstract:
If $M$ is an open connected manifold and $h$ is a homeomorphism of $M$ onto itself such that $h$ is positively regular on $M$ and the set of irregular points, $\operatorname {Irr} (h)$, is a nonseparating compactum, then it is shown that $\operatorname {Irr} (h)$ is a strong deformation retract of $M$.References
- P. F. Duvall Jr. and L. S. Husch, Taming irregular sets of homeomorphisms, Bull. Amer. Math. Soc. 78 (1972), 77–79. MR 290377, DOI 10.1090/S0002-9904-1972-12862-3 —, Homeomorphisms with polyhedral irregular sets, Trans. Amer. Math. Soc. (to appear).
- P. F. Duvall Jr. and L. S. Husch, Analysis on topological manifolds, Fund. Math. 77 (1972), no. 1, 75–90. MR 367952, DOI 10.4064/fm-77-1-75-90
- Sze-tsen Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. MR 0181977 L. S. Husch, Equicontinuous commutative semigroups of onto functions (submitted).
- S. K. Kaul, On almost regular homeomorphisms, Canadian J. Math. 20 (1968), 1–6. MR 222858, DOI 10.4153/CJM-1968-001-5 A. B. Paalman-de Miranda, Topological semigroups, Mathematisch Centrum, Amsterdam, 1970.
- L. S. Pontryagin, Topological groups, Gordon and Breach Science Publishers, Inc., New York-London-Paris, 1966. Translated from the second Russian edition by Arlen Brown. MR 0201557
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 419-422
- MSC: Primary 54C55
- DOI: https://doi.org/10.1090/S0002-9939-1973-0312458-0
- MathSciNet review: 0312458