The Separable Complementation Property and Mrówka Compacta
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 $SCP$.
1985 ◽
Vol 38
(2)
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pp. 198-206
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1985 ◽
Vol 37
(4)
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pp. 730-746
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1977 ◽
Vol 81
(3)
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pp. 523-523
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1987 ◽
Vol 101
(3)
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pp. 385-393
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1983 ◽
Vol 93
(1)
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pp. 1-7
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2012 ◽
Vol 64
(6)
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pp. 1378-1394
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