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- W4255655585 abstract "Publisher SummaryA representation of a normally connected set preserving the limiting element relations is called a continuous representation. If a continuous one-one representation of a normally connected set exists on another normally connected set, the two sets possess the same coherence type. All countable sets of points lying everywhere dense on the open straight line possess the same coherence type η. The conception of dimension can be saved, for the everywhere dense, countable sets of points, by replacing the notion of coherence type by the notion of geometric type. Two sets of points possess the same geometric type, if a uniformly continuous one-one correspondence exists between them. This chapter presents the two principal theorems about the notion of inner limiting set, that is, the set of all the points common to a series of sets of regions— (1) an inner limiting set containing a component dense in itself, has the continuous potency; and (2) a countable set containing no component dense in itself, is an inner limiting set. Each of the successive adherences of a set of points consists of points that are limiting points of every preceding adherence." @default.
- W4255655585 created "2022-05-12" @default.
- W4255655585 date "1976-01-01" @default.
- W4255655585 modified "2023-09-23" @default.
- W4255655585 title "Cantor–Schoenflies style topology" @default.
- W4255655585 doi "https://doi.org/10.1016/b978-0-444-10643-8.50011-7" @default.
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