Some remarks on sequence selection properties using ideals

Abstract

In this paper we follow the line of recent works of Das and hisco-authors where certain results on open covers andselection principles were studied byusing the notion of ideals and ideal convergence, whichautomatically extend similar classical results (where finite setsare used). Here we further introduce the notions of$ıc$-Sequence Selection Property ($ıc$-SSP), $ıc$-MonotonicSequence Selection Property ($ıc$-MSSP) of $C_p(X)$ which extend thenotions of Sequence Selection Property and Monotonic SequenceSelection Property of $C_p(X)$ respectively. We then make certain observationson these new types of SSP in terms of $\mathcal{I}\text{tx}\mathcal{-}\gamma$-covers.