Two classes of FrĂ©chet-Urysohn spaces

Author:
Alan Dow

Journal:
Proc. Amer. Math. Soc. **108** (1990), 241-247

MSC:
Primary 54E35; Secondary 03E35, 03E75, 54A35

DOI:
https://doi.org/10.1090/S0002-9939-1990-0975638-7

MathSciNet review:
975638

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Arhangelâ€™skii introduced five classes of spaces, ${\alpha _i}$-spaces $\left ( {i < 5} \right )$, which are important in the study of products of FrĂ©chet-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 FrĂ©chet-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,
<IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$v$">-space,
<IMG WIDTH="21" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$w$">-space

Article copyright:
© Copyright 1990
American Mathematical Society