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## Cardinal p and a theorem of Pelczynski

## Published Web Location

https://arxiv.org/pdf/math/0006197.pdfNo data is associated with this publication.

## Abstract

We show that it is consistent that for some uncountable cardinal k, all compactifications of the countable discrete space with remainders homeomorphic to $D^k$ are homeomorphic to each other. On the other hand, there are $2^c$ pairwise non-homeomorphic compactifications of the countable discrete space with remainders homeomorphic to $D^c$ (where c is the cardinality of the continuum).