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https://hdl.handle.net/10316/13653
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. | URI: | https://hdl.handle.net/10316/13653 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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On strong inclusions and asymmetric proximities in frames.pdf | 142.49 kB | Adobe PDF | View/Open |
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