Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

On Selectively Star-Lindelof Properties


Affiliations
1 ICFAI University Tripura, Kamalghat, Tripura, 799210, India
2 Department of Mathematics, Tripura University, Suryamaninagar, Tripura, 799022, India
3 Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand
     

   Subscribe/Renew Journal


In this paper a new covering notion, called M-star-Lindelof, is introduced and studied. This notion of covering arises from the selection hypothesis SS*D,fin(D, D). The stronger form SS*D,1(D, D) of the selection hypothesis SS*D,fin(D, D) will also be discussed. We then consider weaker versions of these properties involving iterations of the star operator.

Keywords

Selection Hypothesis, Star-Lindelof Space.
Subscription Login to verify subscription
User
Notifications
Font Size


  • Alas O. T., Junqueira L. R., Wilson R. G., Countability and star covering properties, Topology Appl., 158 (2011) 620-626.
  • Arhangel'skii A.V., Hurewicz spaces, analytic sets and fan-tightness of spaces of functions, Soviet Math. Dokl. 33 (2) (1986) 396-399.
  • Arhangel'skii A.V., Bella A., Countable fan-tightness versus countable tightness, Comment. Math. Univ. Caroline, 37(3) (1996) 567-578.
  • Bal P., Bhowmik S., Star-selection Principle: Another new direction., Journal of the Indian Math. Soc, 84(1-2)(2017) 01-05.
  • Bal P., Bhowmik S., On R-star Lindelof spaces., Palestine Journal of Mathematics, 6(2) (2017) 480-486.
  • Bella A., Bonanzinga M., Matveev M., Variations of selective separability, Topology Appl. 156 (7) (2009) 1241-1252.
  • Caserta, A., Di Maio, G., Kocinac, L. D. R., Meccariello, E, Applications of k-covers, II, Topology Appl. 153 (7) (2006) 3277-3293.
  • Douwen E.K. van, Reed G.M., Roscoe A.W., Tree I.J., Star covering properties, Topology Appl. 39 (1991) 71-103.
  • Engelking R., General topology, Heldermann Verlag (1989).
  • Gauld, David and Mynard, Frederic, Metrisability of manifolds in terms of function spaces, Houston J. Math., 31 (2005) 199-214.
  • Hodel R., Cardinal Functions I, Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds), Elsevier, 1984, 1-61.
  • Hurewicz W., Uber die Verallgemeinerung des Borelschen Theorems , Mathematische Zeitschrift, 24 (1925), 401-425.
  • Kunen K., Set Theory, An Introduction to Independence Proofs, 1e, North-Holland, New York, 1980.
  • McCoy, Robert A. and Ntantu, Ibula, Topological properties of spaces of continuous functions, Lecture Notes in Mathematics 1315, Springer-Verlag, Berlin, 1988.
  • Sakai M., Property Cn and function spaces, Proc. Amer. Math. Soc., 104 (1988), 917919.
  • Scheepers M., Combinatorics of open covers. VI. Selectors for sequences of dense sets, Quaest. Math. 22 (1) (1999)109-130.

Abstract Views: 231

PDF Views: 3




  • On Selectively Star-Lindelof Properties

Abstract Views: 231  |  PDF Views: 3

Authors

Prasenjit Bal
ICFAI University Tripura, Kamalghat, Tripura, 799210, India
Subrata Bhowmik
Department of Mathematics, Tripura University, Suryamaninagar, Tripura, 799022, India
David Gauld
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand

Abstract


In this paper a new covering notion, called M-star-Lindelof, is introduced and studied. This notion of covering arises from the selection hypothesis SS*D,fin(D, D). The stronger form SS*D,1(D, D) of the selection hypothesis SS*D,fin(D, D) will also be discussed. We then consider weaker versions of these properties involving iterations of the star operator.

Keywords


Selection Hypothesis, Star-Lindelof Space.

References