On isomorphic groups and homeomorphic spaces

J. S. Yang
1974 Proceedings of the American Mathematical Society  
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 Sß-pairs.
doi:10.1090/s0002-9939-1974-0339060-x fatcat:yptcab74mbcjjkb2sl5hufdbga