Variations of selective separability and tightness in function spaces with set-open topologies

Abstract

We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.

More on Selective Covering Properties in Bitopological Spaces

“…e first study of weak covering properties in the bitopological context began with the study [20] on the almost Menger property in bitopological spaces and continued in [21,22] where some results on almost Menger and weak Menger properties in the bitopological spaces were obtained. Selective properties in bitopological spaces have been studied in [23][24][25].…”

Neighbourhood star selection properties in bitopological spaces

“…Selective properties in bitopological spaces have been studied in [17,20,21], and for weak covering properties in the bitopological context the study began with the paper [22] on the almost Menger property and continued in [7,8].…”

“…In this paper we extend this investigation and introduce and study neighbourhood star selection (covering) properties in bitopological spaces and so complement research in bitopological context. Let us mention that bitopological selection principles have been discussed in a number of papers [16,17,[20][21][22].…”

Selection principles and games in bitopological function spaces

“…The symbol 0 denotes the constantly zero function in C(X). [13] for λ = k and µ = p) For a space X the following are equivalent:…”