Cardinal functions and mappings associated with the space of quasi-continuous functions equipped with topology of point-wise convergence

TL;DR

This paper studies the cardinal functions of spaces of quasi-continuous functions with pointwise convergence topology, analyzing their topological properties and related maps to deepen understanding of these function spaces.

Contribution

It provides new results on cardinal functions and properties of restriction and induced maps for quasi-continuous function spaces.

Findings

Determined the network weight and Lindelöf degree of $Q_{P}(X)$ and $Q_{P}(X,Y)$.

Analyzed the tightness, pseudocharacter, and $i$-weight of these spaces.

Explored properties of restriction and induced maps related to quasi-continuous functions.

Abstract

Cardinal functions provide valuable insight into the topological properties of spaces, helping to analyze and compare spaces in terms of their covering, convergence and separation properties. This paper focuses on investigating cardinal functions like network weight, Lindel\"of degree, tightness, weak covering, pseudocharacter, and $i$-weight, for the spaces $Q_{P}(X)$ and $Q_{P}(X,Y)$ of quasi-continuous functions under the topology of point-wise convergence. In addition to these, we also investigate properties of restriction and induced maps associated with the spaces $Q_{P}(X)$ and $Q_{P}(X,Y)$.