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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Two classes of Fréchet-Urysohn spaces
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by Alan Dow PDF
Proc. Amer. Math. Soc. 108 (1990), 241-247 Request permission


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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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 241-247
  • MSC: Primary 54E35; Secondary 03E35, 03E75, 54A35
  • DOI:
  • MathSciNet review: 975638