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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Properties of standard maps
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by Gary M. Huckabay PDF
Proc. Amer. Math. Soc. 64 (1977), 169-172 Request permission

Abstract:

Let X and Y be compact metric spaces. Let $S(X,Y)$ denote the collection of standard maps of X onto Y. We establish that $S(C,Y)$ is a dense subset of $C(C,Y)$, where C is the Cantor set. If f is a standard map and $G(f,Y)\{ A(f,Y)\}$ denotes the subgroup of $H(X)$ which preserves {interchanges} the point-inverses of f, then there is a continuous homomorphism of $A(f,Y)$ into $H(Y)$ with kernel $G(f,Y)$. We also show that $G(f,Y)$ and $A(f,Y)$ are closed subsets of $H(X)$.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 169-172
  • MSC: Primary 54C10
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0440490-9
  • MathSciNet review: 0440490