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$\mathscr{R}$-compact spaces with ${\text{\rm\,weight\,}}X < {\text{\rm Exp}{}_{\mathscr{R}} X}$

Author(s): S. Mrowka
Journal: Proc. Amer. Math. Soc. 128 (2000), 3701-3709.
MSC (2000): Primary 54A25; Secondary 54B10, 54G20
Posted: June 7, 2000
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Abstract: Answering a question of Arhangel'skii, we show - under GCH - that for most cardinals $\mathfrak{m}$ there exists an $\mathscr{R}$-compact space $X$ such that ${\text{\rm\,weight\,}}X = \mathfrak{m}$ but $X$ does not embed in a closed fashion into the product of $\mathfrak{m}$ copies of $\mathscr{R}$.

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Additional Information:

S. Mrowka
Affiliation: Department of Mathematics, SUNY at Buffalo, 134 Defendorf Hall, Buffalo, New York 14224
Email: mrowka@acsu.buffalo.edu

DOI: 10.1090/S0002-9939-00-05460-5
PII: S 0002-9939(00)05460-5
Keywords: $\mathscr{R}$- and $\mathscr{N}$-compact spaces, large exponent, $E$-defect, $\eta _{\alpha }$-sets
Received by editor(s): June 3, 1998
Received by editor(s) in revised form: February 2, 1999
Posted: June 7, 2000
Communicated by: Alan Dow
Copyright of article: Copyright 2000, American Mathematical Society

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