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• W2196005512 abstract "Finding a topological space containing a given thing is part of many constructions in topology and has already attracted a lot of attention in the topological past. Unless stated otherwise, all spaces in this chapter are assumed to be completely regular. Completeness is described by Cauchy sequences that depend on the metric. For a completely regular Hausdorff space Z, a compactification of X is a compact space K such that X is homeomorphic to a dense subspace of K. Partially ordered sets of compactifications are extremely important. There are several ways to describe (or generate) constructions of compactifications. The approach of Smirnovís Theorem involves the use of proximities. A lot of effort was concentrated on the question of whether every completely regular scattered space has a scattered compactifcation. A first-countable zero-dimensional Lindelöf Hausdorff space is scattered if it admits a scattered compactification. According to Terada and Terasawa, a first-countable space X is maximal with respect to first-countability. Arkhangelíski showed that each completely regular space X can be embedded in a Hausdorff countably compact space." @default.
• W2196005512 created "2016-06-24" @default.
• W2196005512 creator A5032457397 @default.
• W2196005512 date "2003-01-01" @default.
• W2196005512 modified "2023-09-26" @default.
• W2196005512 title "Extensions of Topological Spaces" @default.
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• W2196005512 doi "https://doi.org/10.1016/b978-044450355-8/50056-8" @default.
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