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

Open Mathematics (2012)

- Volume: 10, Issue: 3, page 1067-1070
- ISSN: 2391-5455

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topZuoming Yu. "A note on the extent of two subclasses of star countable spaces." Open Mathematics 10.3 (2012): 1067-1070. <http://eudml.org/doc/269179>.

@article{ZuomingYu2012,

abstract = {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.},

author = {Zuoming Yu},

journal = {Open Mathematics},

keywords = {Star countable; Strongly monotonically monolithic; Lindelöf; Star compact; star countable; strongly monotonically monolithic; star compact},

language = {eng},

number = {3},

pages = {1067-1070},

title = {A note on the extent of two subclasses of star countable spaces},

url = {http://eudml.org/doc/269179},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Zuoming Yu

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

JO - Open Mathematics

PY - 2012

VL - 10

IS - 3

SP - 1067

EP - 1070

AB - 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.

LA - eng

KW - Star countable; Strongly monotonically monolithic; Lindelöf; Star compact; star countable; strongly monotonically monolithic; star compact

UR - http://eudml.org/doc/269179

ER -

## References

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- [2] van Douwen E.K., Reed G.M., Roscoe, A.W., Tree I.J., Star covering properties, Topology Appl., 1991, 39(1), 71–103 http://dx.doi.org/10.1016/0166-8641(91)90077-Y Zbl0743.54007
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- [4] Gruenhage G., The story of a topological game, Rocky Mountain J. Math., 2006, 36(6), 1885–1914 http://dx.doi.org/10.1216/rmjm/1181069351 Zbl1141.54020
- [5] Heath R.W., Lindgren W.F., Weakly uniform bases, Houston J. Math., 1976, 2(1), 85–90 Zbl0318.54032
- [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 Zbl1131.54022
- [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 Zbl1165.54009

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