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SOME REMARKS ON CENTERED-LINDELÖF SPACES

  • Song, Yan-Kui (DEPARTMENT OF MATHEMATICS NANJING NORMAL UNIVERSITY)
  • Published : 2009.04.30

Abstract

In this paper, we prove the following two statements: (1) There exists a Hausdorff locally $Lindel{\ddot{o}}f$ centered-$Lindel{\ddot{o}}f$ space that is not star-$Lindel{\ddot{o}}f$. (2) There exists a $T_1$ locally compact centered-$Lindel{\ddot{o}}f$ space that is not star-$Lindel{\ddot{o}}f$. The two statements give a partial answer to Bonanzinga and Matveev [2, Question 1].

References

  1. M. Bonanzinga, Star-Lindelof and absolutely star-Lindelof spaces, Questions Answers Gen. Topo-logy. 16 (1998), 79–104
  2. M. Bonanzinga and M. V. Matveev, Centered-Lindelofness versus star-Lindelofness, Comment. Math. Univ. Carolinae. 41 (2000), no. 1, 111–122
  3. M. Bonanzinga and M. V. Matveev, Closed subspaces of star-Lindelof and related spaces, East-West J. Math 2 (2002), no. 1, 171–179
  4. M. Bonanzinga and M. V. Matveev, Products of star-Lindelof and related spaces, Houston J. Math. 27 (2001), 45–57
  5. E. K. van Douwen, G. K. Reed, A. W. Roscoe, and I. J. Tree, Star covering properties, Topology Appl. 39 (1991), 71–103 https://doi.org/10.1016/0166-8641(91)90077-Y
  6. E. Engelking, General Topology, Revised and Completed Edition, Heldermann Verlag, Berlin, 1989
  7. M. V. Matveev, A Survey on Star-Covering Properties, Topological Atlas, preprint No. 330, 1998
  8. Y.-K. Song, Closed subsets of absolutely star-Lindel of spaces II, Comment. Math. Univ. Carolinae. 42 (2003), no. 2, 329–334