Star version of selective menger spaces

P. Gnanachandra; L. Mahalakshmi

doi:10.26637/MJM0604/0017

Abstract

In this paper, we discuss the star version of selective Menger spaces namely R-star-Menger spaces which has been illustrated by suitable examples and investigates some of its topological properties.

Keywords:

R-star Menger Space, R-separable, R-2-star Menger, Star- separable, Countable fan tightness

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

P. Gnanachandra Centre for Research and Post Graduate Studies in Mathematics, Ayya Nadar Janaki Ammal College(Autonomous), Sivakasi-626124,Tamil Nadu, India. https://orcid.org/0000-0001-6089-6441
L. Mahalakshmi Centre for Research and Post Graduate Studies in Mathematics, Ayya Nadar Janaki Ammal College(Autonomous), Sivakasi-626124,Tamil Nadu, India.

Pages: 811-815
Date Published: 01-10-2018
Vol. 6 No. 04 (2018): Malaya Journal of Matematik (MJM)

A.V. Arhangelskii, A theorem on cardinality, Russian Mathematical Surveys, 34 (1979), 153-154.

T. Banakh, On index of total boundedness of (strictly) o-bounded groups, Topology Appl., 120(2002), 427-439.

M. Bonanzinga, and B.A. Pansera, Relative versions of some star-selection principles, Acta Math. Hungar, $117(2007), 231-243$.

M. Bonanzinga, and M.V. Matveev, Some covering properties for $psi$-spaces, Mat. Vesnik., 61(2009), 3-11.

L. Babinkostova, B.A.Pansera, and M.Scheepers, Weak covering properties and selection principles, Topology and its Applications, 160 (2013), 2251-3657.

L. Babinkostova, and M. Scheepers, Combinatorics of open covers (IX) Basis properties, de Matematica, $22(2003), 34-40$.

J.-L. Cao, and Y.-K. Song, Aquaro number versus absolute star-Lindelöf number, Houston J.Math., 29(2003), $925-936$.

A. Caserta, and S. Watson, Alexandroff duplicate and its subspaces, Appl. Gen. Topol., 8(2)(2007), 187-205.

P. Daniels, Pixley-Roy spaces over subsets of the reals, Topology and its Applications, 29(1)(1988), 93-106.

R. Engelking, General Topology, Heldermann Verlag, Berlin, Sigma series in pure Mathematics 6, 1989.

W.M. Fleishman, A new extension of countable compactness, Fund. Math., 67(1)(1970), 1-19.

Fleischman W.M., A new extension of countable compactness, Fund. Math., 67(1971), 1-7.

S. Ikenaga, A class which contains Lindelof spaces, separable spaces and countably compact spaces, $mathrm{Mem} . mathrm{Nu}$ mazu College Tech., 18(1983), 105-108.

J.R. Munkres, Topology, Second Edition, 2000.

W. Just, M.V. Matveev, and P.J. Szeptycki, Some results on property (a), Topology Appl., 101(1)(2000), 103-111.

LJ.D.R. Kočinac, star-Menger and related spaces II, Filomat, 13(1999), 129-140.

Lj. Kočinac, Star-Menger and related spaces, Publ. Math. Debrecen, 55(1999), 421-431.

D. Kocev, Almost Menger and related spaces, Matematički Vesnik, 61(2009), 173-180.

Lj.D.R.kočinac, Selected results on selection principles, In: Proc. Third Seminar Geom.Topol., (2004), 15-17, Tabriz, 71-104.

Lj.D.R.kočinac, Star selection principles: A survey, Khayyam J.Math., I( 2015), 82-106.

A. Lelek, Some cover properties of spaces, Fundamenta Matematicae, 64(1969), 209-218.

K.Menger, Einige überdeckungssätze der Punltmengenlehre, Sitzungberichte Abt.2a, Mathematik, Astronomie, Physik, Meteorologie and Mechanik (Wiener Akademie, Wien) 133 (1924) $421=444$

M.V. Matveev, A survey on star-covering properties, Topology Atlas, preprint No 330, (1998).

L.A.Steen, and J.A.Seebach, Counter examples in Topology, New York, 1995.

M.Scheepers, Combinatorics of open covers (I): theory, Topology and its Applications, 69(1996), 31-62.

M.Scheepers, Combinatorics of open covers (VI): selectors for sequences of dense sets, Quaest.Math., 22(1999), $109-130$.

Shinji Kawaguchi, On Strictly Star-Lindeof Spaces, Scientiae Mathematicae Japonicae, 2006, 1303-1313.

Y.-K. Song, On countable star-covering properties, Appl. Gen. Topol., 8(2)(2007), 249-258.

E.K. Van Douwen, and W.F.Pfeffer, Some properties of the Sorgenfrey line and related spaces, Pacific Journal of Mathematics, 81(1979), 371-377.

Van Douwen E., The integers and topology, Handbook of Set-theoretic Topology (K. Kunen and J.E.Vaughaneds.), North-Holland, Amsterdam, 1984, 111-167.

E.K. Van Douwen, G.K. Reed, A.W. Roscoe, and I.J.Tree, Star covering properties, Topology Appl., 39(1991), 71103.

A. Wilansky, Topics in Fanctional Analysis, Springer, Berlin, 1967.

R.C. Walker, The Stone-Čech compactification, Berlin, (1974).

Yan-Kui Song, On Relative Star-Lindelof Spaces, New Zealand Journal Of Mathematics, 34(2005), 159-163.

Yan-Kui Song, Remarks on strongly star-Menger spaces, Comment. Math. Univ. Carolin., 54(1)(2013), 97-104.

Yan-Kui Song, Remarks on Star-Menger Spaces II, Houston Journal of Mathematics, 40 (2014), 917-925.

Yan-Kui Song, On star-K-Menger spaces, Hacettepe Journal of Mathematics and Statistics, 43(2014), 769-776.

Yan-Kui Song, On Star-C-Menger Spaces, Quaestiones Mathematicae, 37(2014), 337-347.

Yan-Kui Song, Some Remarks On Almost Star Countable Spaces, Studia Scientiarum Mathematicarum Hungarica, 52(2015), 12-20.

Yan-Kui Song, Remarks on Star-Menger Spaces II, Houston Journal of Mathematics, 41 (2015), 357-366.

Yan-Kui Song, Some Remarks On Almost Menger Spaces and Weakly Menger Spaces, Publications De Linstitute Mathematique Nouvelle sérietome, 98 (2015), 193-198.