Title:
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Notes on strongly Whyburn spaces (English) |
Author:
|
Sakai, Masami |
Language:
|
English |
Journal:
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Commentationes Mathematicae Universitatis Carolinae |
ISSN:
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0010-2628 (print) |
ISSN:
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1213-7243 (online) |
Volume:
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57 |
Issue:
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1 |
Year:
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2016 |
Pages:
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123-129 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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:
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Whyburn |
Keyword:
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strongly Whyburn |
Keyword:
|
Fréchet-Urysohn |
MSC:
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54A25 |
MSC:
|
54D55 |
idZBL:
|
Zbl 06562202 |
idMR:
|
MR3478345 |
DOI:
|
10.14712/1213-7243.2015.139 |
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Date available:
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2016-04-12T05:10:16Z |
Last updated:
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2020-01-05 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/144921 |
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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 |
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