Bases and homeomorphisms in polytopological spaces (Q2714361)

The notion of \(r\)-space was introduced by \textit{I. Zuzčák} [Math. Slovaca 33, 249--256 (1983; Zbl 0533.54001)] as a generalization of the notion of a topological space. It is not difficult to prove that if \((X,{\mathcal T}_i)\), \(i=1,\dots, n\), are topological spaces then \((X,{\mathcal T})\), where \({\mathcal T}=\bigcup_{i=1}^n{\mathcal T}_i\), is an \(r\)-space. Such special \(r\)-spaces are called polytopological spaces. In the paper under review the notions of polytopological base of order \(k\) and of \(r\)-base are introduced and studied. Some applications about continuity of maps between polytopological spaces are obtained.