L-spaces and S-spaces in P(ω) |
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Authors: | Eric K van Douwen Kenneth Kunen |
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Institution: | Institute for Medicine and Mathematics, Ohio University, Athens, OH 45701, USA;Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA |
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Abstract: | We show that CH implies that , when equipped with the Vietoris topology, has a subspace which is an L-space and a subspace which is an S-space. This is an immediate consequence of the following purely combinatorial result: CH implies the existence of an ω1-sequence 〈xα: α < ω1〉 in such that (1) if α<β<ω1, then ; (2) if I ?ω1 is unaccountable, then there are distinct α, β ∈ I with Xβ ?Xα. |
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Keywords: | 54A25 54B20 03E05 S-space L-space Vietoris topology cantor topology left separated right separated CH |
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