Ideal quasi-normal convergence and related notions

Lev Bukovský ¹   ; Pratulananda Das ²   ; Jaroslav Šupina ¹

¹ Institute of Mathematics Faculty of Sciences P. J. Šafárik University Jesenná 5 040 01 Košice, Slovakia
² Department of Mathematics Jadavpur University Jadavpur, Kolkata–32, West Bengal, India

Colloquium Mathematicum, Tome 146 (2017) no. 2, pp. 265-281

Résumé

Recently the second author and D. Chandra (2013) began to study the notion of ideal quasi-normal convergence and some topological notions defined by this convergence. We show how some properties of those notions depend on the ideal; sometimes, they are also equivalent to some property of the ideal. Moreover, we exhibit non-trivial cases when the new notion introduced by the ideal quasi-normal convergence is equivalent to the corresponding original notions. Some relations between the new notions for different ideals are investigated as well. Then we extend the characterization of some of the notions by convergence properties of the topological space ${\rm C}_p({X})$. Finally, we study the relation of the new convergences to the covering properties of the underlying topological space.

Détail

DOI : 10.4064/cm6520-3-2016

Keywords: recently second author nbsp chandra nbsp began study notion ideal quasi normal convergence topological notions defined convergence properties those notions depend ideal sometimes equivalent property ideal moreover exhibit non trivial cases notion introduced ideal quasi normal convergence equivalent corresponding original notions relations between notions different ideals investigated extend characterization notions convergence properties topological space finally study relation convergences covering properties underlying topological space