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For a locally compact Hausdorff space K and a Banach space X, let  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 , we denote  as . If  be an extremely regular subspace of  and  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 , then the cardinality of K is less than that of S. Moreover, if  and  is also a subalgebra of , the cardinality of the αth derivative of K is less than that of the αth derivative of S, for each ordinal  Finally, if  and , then K is a continuous image of a subspace of S. Here,  is the geometrical parameter introduced by Jarosz in 1989:  As a consequence, we improve classical results about into isomorphisms from extremely regular subspaces already obtained by Cengiz.

international journal of mathematics and mathematical sciences

Isomorphisms from Extremely Regular Subspaces of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>K</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math> into <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml…

Isomorphisms from Extremely Regular Subspaces of C0K into C0