Previous |  Up |  Next

Article

Title: Notes on strongly Whyburn spaces (English)
Author: Sakai, Masami
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 57
Issue: 1
Year: 2016
Pages: 123-129
Summary lang: English
.
Category: math
.
Summary: We introduce the notion of a strongly Whyburn space, and show that a space $X$ is strongly Whyburn if and only if $X\times(\omega+1)$ is Whyburn. We also show that if $X\times Y$ is Whyburn for any Whyburn space $Y$, then $X$ is discrete. (English)
Keyword: Whyburn
Keyword: strongly Whyburn
Keyword: Fréchet-Urysohn
MSC: 54A25
MSC: 54D55
idZBL: Zbl 06562202
idMR: MR3478345
DOI: 10.14712/1213-7243.2015.139
.
Date available: 2016-04-12T05:10:16Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/144921
.
Reference: [1] Arhangel'skii A.V.: A characterization of very $k$-spaces.Czechoslovak Math. J. 18 (1968), 392–395. MR 0229194
Reference: [2] Arhangel'skii A.V.: Hurewicz spaces, analytic sets and fan tightness of function spaces.Soviet Math. Dokl. 33 (1986), 396–399.
Reference: [3] Aull C.E.: Accessibility spaces, $k$-spaces and initial topologies.Czechoslovak Math. J. 29 (1979), 178–186. MR 0529506
Reference: [4] Bella A., Costantini C., Spadaro S.: P-spaces and the Whyburn property.Houston J. Math. 37 (2011), 995–1015. MR 2844462
Reference: [5] Bella A., Yaschenko I.V.: On AP and WAP spaces.Comment. Math. Univ. Carolin. 40 (1999), 531–536. Zbl 1010.54040, MR 1732483
Reference: [6] Engelking R.: General Topology.revised and completed edition, Helderman Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321
Reference: [7] Gillman L., Jerison M.: Rings of continuous functions.reprint of the 1960 edition, Graduate Texts in Mathematics, 43, Springer, New York-Heidelberg, 1976. Zbl 0327.46040, MR 0407579
Reference: [8] McMillan E.R.: On continuity conditions for functions.Pacific J. Math. 32 (1970), 479–494. MR 0257986, 10.2140/pjm.1970.32.479
Reference: [9] Michael E.: A quintuple quotient quest.Gen. Topology Appl. 2 (1972), 91–138. Zbl 0238.54009, MR 0309045, 10.1016/0016-660X(72)90040-2
Reference: [10] Murtinová E.: On (weakly) Whyburn spaces.Topology Appl. 155 (2008), 2211–2215. MR 2458006, 10.1016/j.topol.2007.05.022
Reference: [11] Nogura T., Tanaka Y.: Spaces which contains a copy of $S_\omega$ or $S_2$ and their applications.Topology Appl. 30 (1988), 51–62. MR 0964062, 10.1016/0166-8641(88)90080-6
Reference: [12] Pelant J., Tkachenko M.G., Tkachuk V.V., Wilson R.G.: Pseudocompact Whyburn spaces need not be Fréchet.Proc. Amer. Math. Soc. 131 (2002), 3257–3265. Zbl 1028.54004, MR 1992867, 10.1090/S0002-9939-02-06840-5
Reference: [13] Pultr A., Tozzi A.: Equationally closed subframes and representations of quotient spaces.Cahiers de Topologie et Géom. Différentielle Catég. 34 (1993), 167–183. MR 1239466
Reference: [14] Siwiec F.: Sequence-covering and countably bi-quotient mappings.Gen. Topology Appl. 1 (1971), 143–154. Zbl 0218.54016, MR 0288737, 10.1016/0016-660X(71)90120-6
Reference: [15] Tkachuk V.V., Yaschenko I.V.: Almost closed sets and topologies they determine.Comment. Math. Univ. Carolin. 42 (2001), 395–405. Zbl 1053.54004, MR 1832158
Reference: [16] Whyburn G.T.: Mappings on inverse sets.Duke Math. J. 23 (1956), 237–240. MR 0098361, 10.1215/S0012-7094-56-02321-3
Reference: [17] Whyburn G.T.: Accessibility spaces.Proc. Amer. Math. Soc. 24 (1970), 181–185. Zbl 0197.48602, MR 0248722, 10.1090/S0002-9939-1970-0248722-0
.

Files

Files Size Format View
CommentatMathUnivCarolRetro_57-2016-1_12.pdf 218.3Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo