# Property D and pseudonormality in first countable spaces

Commentationes Mathematicae Universitatis Carolinae (2005)

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

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topDow, 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

top- Dow A., Set Theory in Topology, in Recent progress in general topology (Prague, 1991); North-Holland, Amsterdam, 1992, pp.167-197. Zbl0796.54001MR1229125
- 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
- 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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