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Title: On strong inclusions and asymmetric proximities in frames
Authors: Picado, Jorge 
Pultr, Aleš 
Keywords: Frame; Biframe; Pseudocomplement; Strong inclusion; Paircover; Quasiuniform frame; Quasi-proximal frame; Total boundedness
Issue Date: 2010
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 10-25 (2010)
Serial title, monograph or event: Pré-Publicações DMUC
Issue: 10-25
Place of publication or event: Coimbra
Abstract: The strong inclusion, a speci c type of subrelation of the order of a lattice with pseudocomplements, has been used in the concrete case of the lattice of open sets in topology for an expedient de nition of proximity, and allowed for a natural point-free extension of this concept. A modi cation of a strong inclusion for biframes then provided a point-free model also for the non-symmetric variant. In this paper we show that a strong inclusion can be non-symmetrically modi ed to work directly on frames, without prior assumption of a biframe structure. The category of quasi-proximal frames thus obtained is shown to be concretely isomorphic with the biframe based one, and shown to be related to that of quasi-uniform frames in a full analogy with the symmetric case.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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