基数p与Pelczynski定理

摘要：

证明了对于不可数基数k，可数离散空间中所有与$D^k$同胚的紧化都是同胚的.另一方面，存在可数离散空间的$2^c$两两非同胚紧化，其中，c是连续统的基数，且它们的邻接者同胚于$D^c$。

英文摘要：

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).

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