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RESEARCH PRODUCT

The Separable Complementation Property and Mrówka Compacta

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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 $SCP$.