Let X, a A, be a collection of topological spaces. Let 3 be the family...

   

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Let X, a € A, be a collection of topological spaces. Let 3 be the family of subsets of IIX of the form IIU, where each U, is an open subset of Xa- Show that IIX, with the box topology, need not be compact, even though each X is compact. Hint: Let each X, be the discrete space consisting of two points. Let X, a € A, be a collection of topological spaces. Let 3 be the family of subsets of IIX of the form IIU, where each U, is an open subset of Xa- Show that IIX, with the box topology, need not be compact, even though each X is compact. Hint: Let each X, be the discrete space consisting of two points.

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