On ω -resolvable and almost- ω -resolvable spaces

J. Angoa; M. Ibarra; Angel Tamariz-Mascarúa

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 3, page 485-508
  • ISSN: 0010-2628

Abstract

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We continue the study of almost- ω -resolvable spaces beginning in A. Tamariz-Mascar’ua, H. Villegas-Rodr’ıguez, Spaces of continuous functions, box products and almost- ω -resoluble spaces, Comment. Math. Univ. Carolin. 43 (2002), no. 4, 687–705. We prove in ZFC: (1) every crowded T 0 space with countable tightness and every T 1 space with π -weight ≤ ℵ 1 is hereditarily almost- ω -resolvable, (2) every crowded paracompact T 2 space which is the closed preimage of a crowded Fréchet T 2 space in such a way that the crowded part of each fiber is ω -resolvable, has this property too, and (3) every Baire dense-hereditarily almost- ω -resolvable space is ω -resolvable. Moreover, by using the concept of almost- ω -resolvability, we obtain two results due the first one to O. Pavlov and the other to V.I. Malykhin: (1) V = L implies that every crowded Baire space is ω -resolvable, and (2) V = L implies that the product of two crowded spaces is resolvable. Finally, we prove that the product of two almost resolvable spaces is resolvable.

How to cite

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Angoa, J., Ibarra, M., and Tamariz-Mascarúa, Angel. "On $\omega $-resolvable and almost-$\omega $-resolvable spaces." Commentationes Mathematicae Universitatis Carolinae 49.3 (2008): 485-508. <http://eudml.org/doc/250302>.

@article{Angoa2008,
abstract = {We continue the study of almost-$\omega $-resolvable spaces beginning in A. Tamariz-Mascar’ua, H. Villegas-Rodr’ıguez, Spaces of continuous functions, box products and almost-$\omega $-resoluble spaces, Comment. Math. Univ. Carolin. 43 (2002), no. 4, 687–705. We prove in ZFC: (1) every crowded $T_0$ space with countable tightness and every $T_1$ space with $\pi $-weight $\le \aleph _1$ is hereditarily almost-$\omega $-resolvable, (2) every crowded paracompact $T_2$ space which is the closed preimage of a crowded Fréchet $T_2$ space in such a way that the crowded part of each fiber is $\omega $-resolvable, has this property too, and (3) every Baire dense-hereditarily almost-$\omega $-resolvable space is $\omega $-resolvable. Moreover, by using the concept of almost-$\omega $-resolvability, we obtain two results due the first one to O. Pavlov and the other to V.I. Malykhin: (1) $V = L$ implies that every crowded Baire space is $\omega $-resolvable, and (2) $V = L$ implies that the product of two crowded spaces is resolvable. Finally, we prove that the product of two almost resolvable spaces is resolvable.},
author = {Angoa, J., Ibarra, M., Tamariz-Mascarúa, Angel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Baire spaces; resolvable spaces; almost resolvable spaces; almost-$\omega $-resolvable spaces; tightness; $\pi $-weight; Baire spaces; resolvable spaces; almost resolvable spaces; tightness; -weight},
language = {eng},
number = {3},
pages = {485-508},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $\omega $-resolvable and almost-$\omega $-resolvable spaces},
url = {http://eudml.org/doc/250302},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Angoa, J.
AU - Ibarra, M.
AU - Tamariz-Mascarúa, Angel
TI - On $\omega $-resolvable and almost-$\omega $-resolvable spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 3
SP - 485
EP - 508
AB - We continue the study of almost-$\omega $-resolvable spaces beginning in A. Tamariz-Mascar’ua, H. Villegas-Rodr’ıguez, Spaces of continuous functions, box products and almost-$\omega $-resoluble spaces, Comment. Math. Univ. Carolin. 43 (2002), no. 4, 687–705. We prove in ZFC: (1) every crowded $T_0$ space with countable tightness and every $T_1$ space with $\pi $-weight $\le \aleph _1$ is hereditarily almost-$\omega $-resolvable, (2) every crowded paracompact $T_2$ space which is the closed preimage of a crowded Fréchet $T_2$ space in such a way that the crowded part of each fiber is $\omega $-resolvable, has this property too, and (3) every Baire dense-hereditarily almost-$\omega $-resolvable space is $\omega $-resolvable. Moreover, by using the concept of almost-$\omega $-resolvability, we obtain two results due the first one to O. Pavlov and the other to V.I. Malykhin: (1) $V = L$ implies that every crowded Baire space is $\omega $-resolvable, and (2) $V = L$ implies that the product of two crowded spaces is resolvable. Finally, we prove that the product of two almost resolvable spaces is resolvable.
LA - eng
KW - Baire spaces; resolvable spaces; almost resolvable spaces; almost-$\omega $-resolvable spaces; tightness; $\pi $-weight; Baire spaces; resolvable spaces; almost resolvable spaces; tightness; -weight
UR - http://eudml.org/doc/250302
ER -

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