Abstract
We discuss three problems of Koszmider on the structure of the spaces of continuous functions on the Stone compact KA generated by an almost disjoint family A of infinite subsets of ω — we present a solution to two problems and develop previous results of Marciszewski and Pol answering the third one. We will show, in particular, that assuming Martin's axiom the space C(KA) is uniquely determined up to isomorphism by the cardinality of A whenever |A|<c, while there are 2c nonisomorphic spaces C(KA) with |A|=c. We also investigate Koszmider's problems in the context of the class of separable Rosenthal compacta and indicate the meaning of our results in the language of twisted sums of c0 and some C(K) spaces.
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