Nearness, Subfitness and Sequential Regularity

H. Herrlich and A. Pultr
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H. Herrlich: Universität Bremen, Fachbereich 3
A. Pultr: Charles University, Department of Applied Mathematics

A chapter in Papers in Honour of Bernhard Banaschewski, 2000, pp 67-80 from Springer

Abstract: Abstract In the point-free context, the structure of nearness has been so far studied in the regular case only. Here we answer the question as to how far beyond that one can go. It turns out that a frame (locale) (quasi-)admits a nearness if it is subfit. Unlike in the case of spaces, where admitting nearness is a hereditary property, subfitness is not; therefore, also the hereditary subfitness (here called sequential regularity for reasons obvious from the properties presented) is studied. It is weaker than regularity and seems to be of some interest also in the spatial case.

Keywords: nearness space; nearnes frame (locale); subfit frame; regular; sequentially regular.; 54A05; 06D10; 54E17; 54D10 (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2529-3_5

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DOI: 10.1007/978-94-017-2529-3_5

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