| Popis: |
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. 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. |
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