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Nearness, Subfitness and Sequential Regularity

In: Papers in Honour of Bernhard Banaschewski

Author

Listed:
  • H. Herrlich

    (Universität Bremen, Fachbereich 3)

  • A. Pultr

    (Charles University, Department of Applied Mathematics)

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.

Suggested Citation

  • H. Herrlich & A. Pultr, 2000. "Nearness, Subfitness and Sequential Regularity," Springer Books, in: Guillaume Brümmer & Christopher Gilmour (ed.), Papers in Honour of Bernhard Banaschewski, pages 67-80, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2529-3_5
    DOI: 10.1007/978-94-017-2529-3_5
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