On some properties of quotients of homogeneous C(K) spaces
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2016, Vol 36, Issue 1
Abstract
We say that an infinite, zero dimensional, compact Hausdorff space K has property (*) if for every nonempty open subset U of K there exists an open and closed subset V of U which is homeomorphic to K. We show that if K is a compact Hausdorff space with property (*) and X is a Banach space which contains a subspace isomorphic to the space C(K) of all scalar (real or complex) continuous functions on K and Y is a closed linear subspace of X which does not contain any subspace isomorphic to the space C([0,1]), then the quotient space X/Y contains a subspace isomorphic to the space C(K).
Authors and Affiliations
Artur Michalak
Keywords
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