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2014 The controlled separable complementation property and monolithic compacta
Jesús Ferrer
Banach J. Math. Anal. 8(2): 67-78 (2014). DOI: 10.15352/bjma/1396640052

Abstract

For a compact $K$, a necessary condition for $C(K)$ to have the Controlled Separable Complementation Property is that $K$ be monolithic. In this paper, we prove that when $K$ contains no copy of $[0,\omega^\omega]$ and the set of points which admit a countable neighborhood base is a cofinite subset of $K$, then monolithicity of $K$ is sufficient for $C(K)$ to enjoy the Controlled Separable Complementation Property. We also show that, for this type of compacta $K$, the space $C(K)$ is separably extensible.

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Jesús Ferrer. "The controlled separable complementation property and monolithic compacta." Banach J. Math. Anal. 8 (2) 67 - 78, 2014. https://doi.org/10.15352/bjma/1396640052

Information

Published: 2014
First available in Project Euclid: 4 April 2014

zbMATH: 1304.46020
MathSciNet: MR3189539
Digital Object Identifier: 10.15352/bjma/1396640052

Subjects:
Primary: 46B10
Secondary: 46B26

Rights: Copyright © 2014 Tusi Mathematical Research Group

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Vol.8 • No. 2 • 2014
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