# (Sub)fit biframes and non-symmetric nearness

@article{Picado2014SubfitBA,
title={(Sub)fit biframes and non-symmetric nearness},
journal={Topology and its Applications},
year={2014},
volume={168},
pages={66-81}
}
• Published 2014
• Mathematics
• Topology and its Applications
Abstract The non-symmetric (quasi-)nearness and its generalized admissibility are studied both in its biframe and paircovers aspect and in the perspective of entourages. The necessary and sufficient condition for a biframe to carry such an enrichment is shown to be a biframe variant of subfitness (resp. fitness, in the hereditary case).
8 Citations
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#### References

SHOWING 1-10 OF 43 REFERENCES
Quasi-nearnesses on biframes and their completions
• Mathematics
• 2010
Abstract We introduce quasi-nearness biframes. They provide a generalization of both nearness frames [5] and quasi-uniform biframes [12]. Quasi-nearness biframes are regular; they are normal if andExpand
The Samuel compactification for quasi-uniform biframes
• Mathematics
• 2009
Abstract The paircover approach is used to explore the links between quasi-uniform and proximal biframes. The Samuel compactification for quasi-uniform biframes is constructed and its universalExpand
Quasi-nearness biframes: unique completions and related covering properties
• Mathematics
• 2012
Abstract Quasi-completeness was considered in [16], where a quasi-completion was constructed for any quasi-nearness biframe. In this paper, we compare the familiar notions of compactness and totalExpand
Nearness, Subfitness and Sequential Regularity
• Mathematics
• 2000
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 frameExpand
Cover quasi-uniformities in frames
• Mathematics
• 2011
Abstract Quasi-uniformities (not necessarily symmetric uniformities) are usually studied via entourages (special neighbourhoods of the diagonal in X × X ) where one can simply forget about theExpand
On Strong Inclusions and Asymmetric Proximities in Frames
• Physics, Computer Science
• Order
• 2012
It is shown that a strong inclusion can be non-symmetrically modified to work directly on frames, without prior assumption of a biframe structure, and the category of quasi-proximal frames is shown to be concretely isomorphic with the biframe based one. Expand
BIFRAMES AND BISPACES
• Mathematics
• 1983
Abstract The concept of a biframe is introduced. Then the known dual adjunction between topological spaces and frames (i.e. local lattices) is extended to one between bispaces (i.e. bitopologicalExpand
Entourages, Covers and Localic Groups
• Mathematics, Computer Science
• Appl. Categorical Struct.
• 2013
It is shown that localic group homomorphisms are uniform, thus providing natural forgetful functors from the category of localic groups into any of the two categories of uniform locales. Expand
Structured Frames by Weil Entourages