Ideal Rothberger spaces

In this paper we introduce Rothberger with respect to an ideal and examine some basic properties. We also investigate its relation to weak Rothberger and almost Rothberger properties.

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  • P. Daniels, Pixley-Roy spaces over subsets of the reals, Topology App. 29(1988)93-106.
  • T.R. Hamlett, Lindelöf with respect to an ideal, New Zealand Journal of Mathematics, 42(2012)115-120.
  • K. Kuratowski, Topology,Vol.1, Academic Press, New York, 1966.
  • D. Jankovic, T.R. Hamlett, New Topologies from old via ideals, Amer. Math. Monthly, 97(1990)295-310.
  • F. Rothberger, Eine Verschärfung der Eigenschalft, Fund. Math. 3(1938)50-55.
  • M. Scheepers, Combinatorics of open covers(I): Ramsey theory, Topology Appl. 69(1996)31- 62.
  • M. Scheepers, Lusin sets, Proc. Amer. Math. Soc., 197(1999)251-257.
  • Y.K. Song, Remarks on almost Rothberger spaces and weakly Rothberger spaces, Quaestiones Mathematicae, 38(3)(2015)317-325.
  • L.A. Steen, J.A. Seebach,Jr., Counterexamples in topology, Dover Publications, Inc., New York, 1978.
  • R. Vaidyanathaswamy, The localisation theory in the set topology, Proc.Indian Acad. Sci. 20(1945),51–61.