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

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 $Q_{P}(X,Y)$.