Characters of countably tight spaces and inaccessible cardinals

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抄録

In this paper, we study some connections between characters of countably tight spaces of size ω1 and inaccessible cardinals. A countable tight space is indestructible if every σ-closed forcing notion preserves countable tightness of the space. We show that, assuming the existence of an inaccessible cardinal, the following statements are consistent:(1)Every indestructibly countably tight space of size ω1 has character ≤ω1.(2)2ω12 and there is no countably tight space of size ω1 and character ω2. For the converse, we show that, if ω2 is not inaccessible in the constructible universe L, then there is an indestructibly countably tight space of size ω1 and character ω2.

本文言語English
ページ(範囲)95-106
ページ数12
ジャーナルTopology and its Applications
161
1
DOI
出版ステータスPublished - 2014
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ASJC Scopus subject areas

  • 幾何学とトポロジー

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