ON QUASI P-SPACES AND THEIR APPLICATIONS IN SUBMAXIMAL AND NODEC SPACES

A topological space is called submaximal if each of its dense subsets is open and is called nodec if each of its nowhere dense subsets is closed. Here, we study a variety of spaces some of which have already been studied in C(X). Among them are, most importantly, quasi P-spaces and pointwise quasi P-spaces. We obtain some new useful topological characterizations of quasi P-spaces and pointwise quasi P-spaces. Consequently, we obtain a close relation between these latter spaces and submaximal and nodec spaces.