Countably metacompact spaces in the constructible universe

Paul Szeptycki

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 3, page 221-230
  • ISSN: 0016-2736

Abstract

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We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a G δ . In addition some nonperfect spaces with σ-disjoint bases are constructed.

How to cite

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Szeptycki, Paul. "Countably metacompact spaces in the constructible universe." Fundamenta Mathematicae 143.3 (1993): 221-230. <http://eudml.org/doc/212006>.

@article{Szeptycki1993,
abstract = {We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a $G_δ$. In addition some nonperfect spaces with σ-disjoint bases are constructed.},
author = {Szeptycki, Paul},
journal = {Fundamenta Mathematicae},
keywords = {countably metacompact; $G_δ$, ♢*; axiom of constructibility; diamond star; countably metacompact space; nonperfect spaces},
language = {eng},
number = {3},
pages = {221-230},
title = {Countably metacompact spaces in the constructible universe},
url = {http://eudml.org/doc/212006},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Szeptycki, Paul
TI - Countably metacompact spaces in the constructible universe
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 3
SP - 221
EP - 230
AB - We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a $G_δ$. In addition some nonperfect spaces with σ-disjoint bases are constructed.
LA - eng
KW - countably metacompact; $G_δ$, ♢*; axiom of constructibility; diamond star; countably metacompact space; nonperfect spaces
UR - http://eudml.org/doc/212006
ER -

References

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  8. [K] K. Kunen, Set Theory, An Introduction to Independence Proofs, North-Holland, Amsterdam, 1980. Zbl0443.03021
  9. [N1] P. Nyikos, A provisional solution to the normal Moore space problem, Proc. Amer. Math. Soc. 78 (1980), 429-435. Zbl0446.54030
  10. [N2] P. Nyikos, Countably metacompact, locally countable spaces in the constructible universe, Topology Appl., to appear. Zbl0893.54017
  11. [S] P. J. Szeptycki, Uncovering separation properties in the Easton model, preprint. Zbl0862.54019
  12. [T1] F. D. Tall, Set-theoretic consistence results and topological theorems concerning the normal Moore space conjecture and related problems, Dissertationes Math. 148 (1977). 
  13. [T2] F. D. Tall, Covering and separation properties in the Easton model, Topology Appl. 28 (1988), 155-163. 
  14. [W] S. Watson, Separation in countably paracompact spaces, Trans. Amer. Math. Soc. 290 (1985), 831-842. Zbl0583.54013

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