A note on the extent of two subclasses of star countable spaces

• Autorzy: Zuoming Yu
• Języki publikacji: EN

Abstrakty

EN

We prove that every Tychonoff strongly monotonically monolithic star countable space is Lindelöf, which solves a question posed by O.T. Alas et al. We also use this result to generalize a metrization theorem for strongly monotonically monolithic spaces. At the end of this paper, we study the extent of star countable spaces with k-in-countable bases, k ∈ ℤ.

Słowa kluczowe

EN

Star countable; Strongly monotonically monolithic; Lindelöf; Star compact

Kategorie tematyczne

• 54D70: Base properties
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 1067-1070

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Zuoming Yu

• Jiangsu University of Science and Technology

Bibliografia

• [1] Alas O.T., Junqueira L.R., van Mill J., Tkachuk V.V., Wilson R.G., On the extent of star countable spaces, Cent. Eur. J. Math., 2011, 9(3), 603–615 http://dx.doi.org/10.2478/s11533-011-0018-y
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• [6] van Mill J., Tkachuk V.V., Wilson R.G., Classes defined by stars and neighbourhood assignments, Topology Appl., 2007, 154(10), 2127–2134 http://dx.doi.org/10.1016/j.topol.2006.03.029
• [7] Tkachuk V.V., Monolithic spaces and D-spaces revisited, Topology Appl., 2009, 156(4), 840–846 http://dx.doi.org/10.1016/j.topol.2008.11.001

Identyfikatory

DOI

10.2478/s11533-012-0030-x