Property D and pseudonormality in first countable spaces

Alan S. Dow

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 2, page 369-372
  • ISSN: 0010-2628

Abstract

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In answer to a question of M. Reed, E. van Douwen and M. Wage [vDW79] constructed an example of a Moore space which had property D but was not pseudonormal. Their construction used the Martin’s Axiom type principle P ( c ) . We show that there is no such space in the usual Cohen model of the failure of CH.

How to cite

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Dow, Alan S.. "Property D and pseudonormality in first countable spaces." Commentationes Mathematicae Universitatis Carolinae 46.2 (2005): 369-372. <http://eudml.org/doc/249563>.

@article{Dow2005,
abstract = {In answer to a question of M. Reed, E. van Douwen and M. Wage [vDW79] constructed an example of a Moore space which had property D but was not pseudonormal. Their construction used the Martin’s Axiom type principle $P(c)$. We show that there is no such space in the usual Cohen model of the failure of CH.},
author = {Dow, Alan S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {property D; pseudonormal; first countable; Cohen model; Cohen model},
language = {eng},
number = {2},
pages = {369-372},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Property D and pseudonormality in first countable spaces},
url = {http://eudml.org/doc/249563},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Dow, Alan S.
TI - Property D and pseudonormality in first countable spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 2
SP - 369
EP - 372
AB - In answer to a question of M. Reed, E. van Douwen and M. Wage [vDW79] constructed an example of a Moore space which had property D but was not pseudonormal. Their construction used the Martin’s Axiom type principle $P(c)$. We show that there is no such space in the usual Cohen model of the failure of CH.
LA - eng
KW - property D; pseudonormal; first countable; Cohen model; Cohen model
UR - http://eudml.org/doc/249563
ER -

References

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  1. Dow A., Set Theory in Topology, in Recent progress in general topology (Prague, 1991); North-Holland, Amsterdam, 1992, pp.167-197. Zbl0796.54001MR1229125
  2. Kunen K., Set Theory, volume 102 of {Studies in Logic and the Foundations of Mathematics}; North-Holland Publishing Co., Amsterdam, 1983; An introduction to independence proofs, Reprint of the 1980 original. Zbl0960.03033MR0597342
  3. van Douwen E.K., Wage M.L., Small subsets of first countable spaces, Fund. Math. 103 2 103-110 (1979). (1979) Zbl0425.54013MR0543872

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