On nearly paralindelöf spaces (Q1176022)

A space \(X\) is called nearly para-Lindelöf if every open cover \({\mathcal U}\) of \(X\) admits a locally countable open refinement \({\mathcal V}\), not necessarily a cover of \(X\), such that \(X= \bigcup \{\text{int cl } V\): \(V\in {\mathcal V}\}\). In this paper, nearly para-Lindelöf spaces are characterized. Several properties of these spaces and their semiregularization are studied and examples are given to establish relationships between the properties ``nearly para-Lindelöf'', ``Lindelöf'', ``nearly Lindelöf'', ``almost Lindelöf'', ``para- Lindelöf'', ``almost para-Lindelöf'' and ``almost regular''.