Abstract

(K, W) = {f If E BA, f(K) C W}, for K a compact subset of A and W an open subset of B [2]1. Now let X and Y be Hausdorff spaces, and let Z be an arbitrary topological space. Let XX Y be the topological product of X and Y. We shall be concerned with the compact-open topologized spaces zxxy Zx, and (Zx)y. R. H. Fox [2] has related these spaces, taking Zx as compact-open topologized, but not considering topologies on the more complex spaces. Our basic result is the following theorem, which, with its corollary, adds significant conclusions to the results of Fox.

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