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 ea subsets is closedý. ýHereý, ýwe study a variety of spaces some of which have already been studied in C(X)ý. ýAmong them areý, ýmost importantlyý, ýquasi P-spaces and pointwise quasi P-spacesý. ýWe obtain some new useful topological characterizations of quasi P-spaces and pointwise quasi P -spacesý. ýConsequentlyý, ýwe obtain a close relation between these latter spaces and submaximal and nodec spacesý.