Abstract

In this paper we follow the line of recent works of Das and his co-authors where certain results on open covers and selection principles were studied by using the notion of ideals and ideal convergence, which automatically extend similar classical results (where finite sets are used). Here we further introduce the notions of $\ic$-Sequence Selection Property ($\ic$-SSP), $\ic$-Monotonic Sequence Selection Property ($\ic$-MSSP) of $C_p(X)$ which extend the notions of Sequence Selection Property and Monotonic Sequence Selection Property of $C_p(X)$ respectively. We then make certain observations on these new types of SSP in terms of $\Cal{I}\tx{-}\gamma$-covers.

Keywords: Ideal convergence; $\ic$-SSP; $\ic$-MSSP; $\iga$-cover; $\ic$-Hurewicz property; $\SONE(\iGa,\iGa)$-space; $\ic\text{-}\gamma\gamma_{co}$-space

MSC: 54G99, 03E05, 54C30, 40G15

Pages:  39$-$44     

Volume  68 ,  Issue  1 ,  2016