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Proceedings of the American Mathematical Society

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



On isomorphic groups and homeomorphic spaces

Author: J. S. Yang
Journal: Proc. Amer. Math. Soc. 43 (1974), 431-438
MSC: Primary 54C35; Secondary 22A05
Erratum: Proc. Amer. Math. Soc. 48 (1975), 517.
MathSciNet review: 0339060
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Abstract: Let $C(X,G)$ denote the group of continuous functions from a topological space $X$ into a topological group $G$ with the pointwise multiplication. Some classes of SQ-pairs and properties of the corresponding topological group $C(X,G)$ with the compact-open topology are investigated. We also show that the existence of a group isomorphism between groups $C(X,G)$ and $C(Y,G)$ implies the existence of a homeomorphism between $X$ and $Y$, if $(X,G)$ and $(Y,G)$ are SQ-pairs.

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Keywords: Topological group, pointwise multiplication, group, isomorphism, homomorphism, <IMG WIDTH="17" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$k$">-space, compact-open topology, jointly continuous
Article copyright: © Copyright 1974 American Mathematical Society