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Isomorphisms from Extremely Regular Subspaces of C0K into C0S,X Spaces

2019
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International Journal of Mathematics and Mathematical Sciences
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For a locally compact Hausdorff space K and a Banach space X, let C0K,X be the Banach space of all X-valued continuous functions defined on K, which vanish at infinite provided with the sup norm. If X is ℝ, we denote C0K,X as C0K. If AK be an extremely regular subspace of C0K and T:AK⟶C0S,X is an into isomorphism, what can be said about the set-theoretical or topological properties of K and S? Answering the question, we will prove that if X contains no copy of c0, then the cardinality of K is

doi:10.1155/2019/7146073
fatcat:hlrdsnoddraibfmccx2dgdfrfq