×

A characterization of almost resolvable spaces. (English) Zbl 0725.54024

The authors prove few simple theorems about almost resolvable spaces and related spaces. Theorem: A space X is almost resolvable if and only if X is the union of two disjoint sets, one of them is resolvable and closed and the other one of 1st category.

MSC:

54E52 Baire category, Baire spaces
54C30 Real-valued functions in general topology
Full Text: DOI

References:

[1] Bolstein R.,Sets of points of discontinuity, Proc. Amer. Math Soc.38, No. 1, 1973. · Zbl 0232.54014
[2] Ceder J.G.,On maximally resolvable spaces, Fund. Math.55 (1964), 87–93. · Zbl 0139.40401
[3] Ceder J.G., Pearson T.L.,On products of maximally resolvable spaces, Pacific J. Math.22 (1967). · Zbl 0153.24201
[4] Hahn H.,Reele Funktionen, Academic Verlagsgesellschaft, Leipzig, 1932, reprint Chelsea, New York, 1948.
[5] Hewitt E.,A problem of set-theoretic topology, Duke Math. J.10 (1943), 309–333, MR 5, 46. · Zbl 0060.39407 · doi:10.1215/S0012-7094-43-01029-4
[6] Hewitt E., Stromberg K.,Real and abstract analysis, A modern treatment of the theory of functions of a real variable, Springer-Verlag, New York, 1965, MR 32 5826. · Zbl 0137.03202
[7] Katetov M.,On topological spaces containing no disjoint dense subsets, Math. Sbornik, N.S.,21 (63), 1947, 3–12.
[8] Kelley J.L.,General Topology, New York, 1955.
[9] Kunen K., Szymanski A., Tall F.,Baire irresolvable spaces and ideal theory, Annales Mathematicae Silesianae 2 (14), Uniwersytet Sloski, Kawotice 1986. · Zbl 0613.54018
[10] Kuratowski C.,Topology, Vol. II, New York and London, 1968.
[11] Malyhin V.I.,On the resolvability of the product of two spaces and a problem of Katetov, (in Russian) Dokl. Akad. Nauk SSSR222 (1975), 725–729. · Zbl 0325.54017
[12] Padmavally K.,An example of a connected irresolvable Hausdorff space, Duke Math. J.20 (1953), 513–520. · Zbl 0052.18904 · doi:10.1215/S0012-7094-53-02050-X
[13] Pearson T.L.,Some sufficient conditions for maximal resolvability, Canad. Math. Bull.14 (1971), 191–196. · Zbl 0212.54604 · doi:10.4153/CMB-1971-034-5
[14] Young W.H.,Uber die Einteilung der unstetigen Funktionen und die Verteilung ihrer Stetigkeitspunkte, S.B. Akad. Wiss. Wien Math.-Natur. K. Abt. IIA112 (1907), 1307–1311. · JFM 34.0411.03
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.