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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Properties of standard maps


Author: Gary M. Huckabay
Journal: Proc. Amer. Math. Soc. 64 (1977), 169-172
MSC: Primary 54C10
MathSciNet review: 0440490
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0440490-9
PII: S 0002-9939(1977)0440490-9
Article copyright: © Copyright 1977 American Mathematical Society