Regular spaces of small extent are ω-resolvable

István Juhász; Lajos Soukup; Zoltán Szentmiklóssy

Fundamenta Mathematicae (2015)

  • Volume: 228, Issue: 1, page 27-46
  • ISSN: 0016-2736

Abstract

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We improve some results of Pavlov and Filatova, concerning a problem of Malykhin, by showing that every regular space X that satisfies Δ(X) > e(X) is ω-resolvable. Here Δ(X), the dispersion character of X, is the smallest size of a non-empty open set in X, and e(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindelöf spaces of uncountable dispersion character are ω-resolvable. We also prove that any regular Lindelöf space X with |X| = Δ(X) = ω₁ is even ω₁-resolvable. The question whether regular Lindelöf spaces of uncountable dispersion character are maximally resolvable remains wide open.

How to cite

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István Juhász, Lajos Soukup, and Zoltán Szentmiklóssy. "Regular spaces of small extent are ω-resolvable." Fundamenta Mathematicae 228.1 (2015): 27-46. <http://eudml.org/doc/282992>.

@article{IstvánJuhász2015,
abstract = { We improve some results of Pavlov and Filatova, concerning a problem of Malykhin, by showing that every regular space X that satisfies Δ(X) > e(X) is ω-resolvable. Here Δ(X), the dispersion character of X, is the smallest size of a non-empty open set in X, and e(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindelöf spaces of uncountable dispersion character are ω-resolvable. We also prove that any regular Lindelöf space X with |X| = Δ(X) = ω₁ is even ω₁-resolvable. The question whether regular Lindelöf spaces of uncountable dispersion character are maximally resolvable remains wide open. },
author = {István Juhász, Lajos Soukup, Zoltán Szentmiklóssy},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {1},
pages = {27-46},
title = {Regular spaces of small extent are ω-resolvable},
url = {http://eudml.org/doc/282992},
volume = {228},
year = {2015},
}

TY - JOUR
AU - István Juhász
AU - Lajos Soukup
AU - Zoltán Szentmiklóssy
TI - Regular spaces of small extent are ω-resolvable
JO - Fundamenta Mathematicae
PY - 2015
VL - 228
IS - 1
SP - 27
EP - 46
AB - We improve some results of Pavlov and Filatova, concerning a problem of Malykhin, by showing that every regular space X that satisfies Δ(X) > e(X) is ω-resolvable. Here Δ(X), the dispersion character of X, is the smallest size of a non-empty open set in X, and e(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindelöf spaces of uncountable dispersion character are ω-resolvable. We also prove that any regular Lindelöf space X with |X| = Δ(X) = ω₁ is even ω₁-resolvable. The question whether regular Lindelöf spaces of uncountable dispersion character are maximally resolvable remains wide open.
LA - eng
UR - http://eudml.org/doc/282992
ER -

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