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 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.