Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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


Author: S. Mrowka
Journal: Proc. Amer. Math. Soc. 128 (2000), 3701-3709
MSC (2000): Primary 54A25; Secondary 54B10, 54G20
DOI: https://doi.org/10.1090/S0002-9939-00-05460-5
Published electronically: June 7, 2000
MathSciNet review: 1690997
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $\mathscr{R}$.


References [Enhancements On Off] (What's this?)

  • [vDou] E.K. van Douwen, The integers and topology, Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 111 - 167. MR 87f:54008
  • [Hec] S.H. Heckler, Exponents of some $\mathscr{N}$-compact spaces, Israel J. Math. 15 (1973), 384 - 395.
  • [Kul] John Kulesza, Metrizable spaces where the inductive dimensions disagree, Trans. A.M.S. 318, no. 2 (1990), 763-781. MR 90g:54030
  • [M1] S. Mrówka, On E-compact spaces II, Bull. Acad. Polon. Sci. 14 (1966), 597 - 605. MR 34:6712
  • [M2] -, Further results on E-compact spaces, Acta Math. 120 (1968), 161 - 185. MR 37:2165
  • [M3] -, Extending of continuous real functions, Compositio Math. 21 (1969), 319 - 327. MR 40:8020
  • [M4] -, $\mathscr{N}$-compactness, metrizability and covering dimension, Rings of continuous functions, Marcell Dekker, Inc., New York and Basel, 1985, pp. 248 - 275. MR 86i:54034
  • [M5] -, Preservation of $E$-compactness, in preparation.
  • [M6] -, Small inductive dimension of completions of metric spaces, Proc. Amer. Math. Soc. 125 (5) (1997), 1545 - 1554. MR 97i:54043
  • [Sik] R. Sikorski, Remarks on some topological spaces of high power, Fund. Math. 37 (1950), 125 - 136. MR 12:727e

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54A25, 54B10, 54G20

Retrieve articles in all journals with MSC (2000): 54A25, 54B10, 54G20


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-00-05460-5
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
Published electronically: June 7, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society