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Article

Keywords:
Whyburn; strongly Whyburn; Fréchet-Urysohn
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.
References:
[1] Arhangel'skii A.V.: A characterization of very $k$-spaces. Czechoslovak Math. J. 18 (1968), 392–395. MR 0229194
[2] Arhangel'skii A.V.: Hurewicz spaces, analytic sets and fan tightness of function spaces. Soviet Math. Dokl. 33 (1986), 396–399.
[3] Aull C.E.: Accessibility spaces, $k$-spaces and initial topologies. Czechoslovak Math. J. 29 (1979), 178–186. MR 0529506
[4] Bella A., Costantini C., Spadaro S.: P-spaces and the Whyburn property. Houston J. Math. 37 (2011), 995–1015. MR 2844462
[5] Bella A., Yaschenko I.V.: On AP and WAP spaces. Comment. Math. Univ. Carolin. 40 (1999), 531–536. MR 1732483 | Zbl 1010.54040
[6] Engelking R.: General Topology. revised and completed edition, Helderman Verlag, Berlin, 1989. MR 1039321 | Zbl 0684.54001
[7] Gillman L., Jerison M.: Rings of continuous functions. reprint of the 1960 edition, Graduate Texts in Mathematics, 43, Springer, New York-Heidelberg, 1976. MR 0407579 | Zbl 0327.46040
[8] McMillan E.R.: On continuity conditions for functions. Pacific J. Math. 32 (1970), 479–494. DOI 10.2140/pjm.1970.32.479 | MR 0257986
[9] Michael E.: A quintuple quotient quest. Gen. Topology Appl. 2 (1972), 91–138. DOI 10.1016/0016-660X(72)90040-2 | MR 0309045 | Zbl 0238.54009
[10] Murtinová E.: On (weakly) Whyburn spaces. Topology Appl. 155 (2008), 2211–2215. DOI 10.1016/j.topol.2007.05.022 | MR 2458006
[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. DOI 10.1016/0166-8641(88)90080-6 | MR 0964062
[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. DOI 10.1090/S0002-9939-02-06840-5 | MR 1992867 | Zbl 1028.54004
[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
[14] Siwiec F.: Sequence-covering and countably bi-quotient mappings. Gen. Topology Appl. 1 (1971), 143–154. DOI 10.1016/0016-660X(71)90120-6 | MR 0288737 | Zbl 0218.54016
[15] Tkachuk V.V., Yaschenko I.V.: Almost closed sets and topologies they determine. Comment. Math. Univ. Carolin. 42 (2001), 395–405. MR 1832158 | Zbl 1053.54004
[16] Whyburn G.T.: Mappings on inverse sets. Duke Math. J. 23 (1956), 237–240. DOI 10.1215/S0012-7094-56-02321-3 | MR 0098361
[17] Whyburn G.T.: Accessibility spaces. Proc. Amer. Math. Soc. 24 (1970), 181–185. DOI 10.1090/S0002-9939-1970-0248722-0 | MR 0248722 | Zbl 0197.48602
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