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• W2049361924 startingPage "219" @default.
• W2049361924 abstract "Properties of spaces in which every subset is open in its closure are investigated. When scattered, such submaximal spaces are nodec (in the sense of van Douwen) and conversely. Every countably compact Hausdorff nodec space is the free topological sum of finitely many Alexandroff compactifications of discrete spaces. Pseudocompact Tychonoff submaximal spaces are shown to be scattered. The authors do not know if there is an infinite regular connected submaximal space, or if there is in ZFC a Hausdorff submaximal topological group, but we prove that every separable Tychonoff submaximal space is totally disconnected. We pay special attention to Lindelöf submaximal spaces, showing, in particular, that pseudo-Lindelöf submaximal spaces are Lindelöf. The last section is devoted to submaximal topological groups, where it is established that each pseudocompact submaximal topological group is finite and each totally bounded submaximal topological group is countable." @default.
• W2049361924 created "2016-06-24" @default.
• W2049361924 creator A5019902087 @default.
• W2049361924 creator A5052874772 @default.
• W2049361924 date "1995-07-01" @default.
• W2049361924 modified "2023-10-18" @default.
• W2049361924 title "On submaximal spaces" @default.
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• W2049361924 doi "https://doi.org/10.1016/0166-8641(94)00093-i" @default.
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