Submaximal and door compactifications

AbstractIn 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.Let X be a topological space and K(X) be a compactification of X.We prove, here, that K(X) is submaximal if and only if for each dense subset D of X, the following properties hold:(i)D is co-finite in K(X);(ii)for each x∈K(X)∖D, {x} is closed.If X is 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