Cardinal p and a theorem of Pelczynski
Abstract
We show that it is consistent that for some uncountable cardinal k, all compactifications of the countable discrete space with remainders homeomorphic to Dk are homeomorphic to each other. On the other hand, there are 2c pairwise non-homeomorphic compactifications of the countable discrete space with remainders homeomorphic to Dc (where c is the cardinality of the continuum).
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