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Two classes of Fréchet-Urysohn spaces

Author: Alan Dow
Journal: Proc. Amer. Math. Soc. 108 (1990), 241-247
MSC: Primary 54E35; Secondary 03E35, 03E75, 54A35
MathSciNet review: 975638
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Abstract: Arhangel'skii introduced five classes of spaces, $ {\alpha _i}$-spaces $ \left( {i < 5} \right)$, which are important in the study of products of Fréchet-Urysohn spaces. For each $ i < 5$, each $ {\alpha _i}$-space is an $ {\alpha _{i + 1}}$-space and it follows from the continuum hypothesis that there are countable $ {\alpha _{i + 1}}$-spaces which are not $ {\alpha _i}$-spaces. A $ v$-space ($ w$-space) is a Fréchet-Urysohn $ {\alpha _1}$-space ( $ {\alpha _2}$-space). We show that there is a model of set theory in which each $ {\alpha _2}$-space ($ w$-space) is an $ {\alpha _1}$-space ($ v$-space).

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Keywords: Fréchet-Urysohn space, $ v$-space, $ w$-space
Article copyright: © Copyright 1990 American Mathematical Society