The Separable Complementation Property and Mr¨®wka Compacta

Jesus Ferrer

Journal of Mathematics Research, 2017, vol. 9, issue 5, 30-36

Abstract: We study the separable complementation property for $C(K_{\cal A})$ spaces when $K_{\cal A}$ is the Mr\'owka compact associated to an almost disjoint family ${\cal A}$ of countable sets. In particular we prove that, if ${\cal A}$ is a generalized ladder system, then $C(K_{\cal A})$ has the separable complementation property ($SCP$ for short) if and only if it has the controlled version of this property. We also show that, when ${\cal A}$ is a maximal generalized ladder system, the space $C(K_{\cal A})$ does not enjoy the $SCP$.

Keywords: Mr\'owka compacta; $mad$ families; Separable Complementation Property (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:9:y:2017:i:5:p:30

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