Submaximal and door compactifications

In this paper, a characterization is given for compact door spaces. We, also, deal with spaces X such that a compactification K ( X ) of X is submaximal or door. be a topological space and K ( X ) be a compactification of X. ve, here, that K ( X ) is submaximal if and only if for each dense subset D of X, the following properties hold:(i) o-finite in K ( X ) ; ch x ∈ K ( X ) ∖ D , { x } is closed. s a noncompact space, then we show that K ( X ) is a door space if and only if X is a discrete space and K ( X ) is the one-point compactification of X.