Some results on expansive mappings
Author:
Richard K. Williams
Journal:
Proc. Amer. Math. Soc. 26 (1970), 655-663
MSC:
Primary 54.82
DOI:
https://doi.org/10.1090/S0002-9939-1970-0266186-8
MathSciNet review:
0266186
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, expansive mappings are seen as generalizations of expansive homeomorphisms, and known theorems are generalized. The nonexistence of expansive functions on the open unit interval is proven, and a new example of an expansive homeomorphism on the open unit disk is given. Finally, a method for constructing expansive homeomorphisms from expansive mappings is given.
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Claude Berge, Topological Spaces, Oliver and Boyd, London, 1963.
- B. F. Bryant, Expansive Self-Homeomorphisms of a Compact Metric Space, Amer. Math. Monthly 69 (1962), no. 5, 386–391. MR 1531676, DOI https://doi.org/10.2307/2312129
- B. F. Bryant, On expansive homeomorphisms, Pacific J. Math. 10 (1960), 1163–1167. MR 120632
- William Reddy, The existence of expansive homeomorphisms on manifolds, Duke Math. J. 32 (1965), 627–632. MR 187226
- W. R. Utz, Unstable homeomorphisms, Proc. Amer. Math. Soc. 1 (1950), 769–774. MR 38022, DOI https://doi.org/10.1090/S0002-9939-1950-0038022-3 Richard K. Williams, Doctoral Thesis, Vanderbilt University, Nashville, Tenn., 1965.
- Richard K. Williams, A note on expansive mappings, Proc. Amer. Math. Soc. 22 (1969), 145–147. MR 242143, DOI https://doi.org/10.1090/S0002-9939-1969-0242143-4
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Additional Information
Keywords:
Expansive function,
expansive mapping,
expansive homeomorphism,
orbit,
iterates,
asymptotic points
Article copyright:
© Copyright 1970
American Mathematical Society