ArticleOriginal scientific text

Title

On some properties of quotients of homogeneous C(K) spaces

Authors 1

Affiliations

  1. Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland

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).

Keywords

nonseparable C(K) spaces, quotients of C(K) spaces

Bibliography

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Pages:
33-43
Main language of publication
English
Received
2016-01-12
Accepted
2016-04-30
Published
2016
Exact and natural sciences