On isomorphic groups and homeomorphic spaces

Yang, J. S.

doi:10.1090/S0002-9939-1974-0339060-X

On isomorphic groups and homeomorphic spaces
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Proc. Amer. Math. Soc. 43 (1974), 431-438 Request permission

Erratum: Proc. Amer. Math. Soc. 48 (1975), 517.

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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