On Selectively Star-Lindelof Properties
DOI:
https://doi.org/10.18311/jims/2018/20145Keywords:
Selection Hypothesis, Star-Lindelof SpaceAbstract
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.Downloads
Metrics
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 Prasenjit Bal, Subrata Bhowmik, David Gauld
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2023-01-30
Published 2018-06-01
References
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.