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

Zuoming Yu

Open Mathematics (2012)

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

Abstract

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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.

How to cite

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Zuoming 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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  1. [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 Zbl1246.54017
  2. [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
  3. [3] Gruenhage G., Infinite games and generalizations of first-countable spaces, General Topology and Appl., 1976, 6(3), 339–352 http://dx.doi.org/10.1016/0016-660X(76)90024-6 
  4. [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. [5] Heath R.W., Lindgren W.F., Weakly uniform bases, Houston J. Math., 1976, 2(1), 85–90 Zbl0318.54032
  6. [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. [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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