(Sub)fit biframes and non-symmetric nearness

Picado, Jorge; Pultr, Aleš

doi:10.1016/j.topol.2014.02.012

Cited by 6 publications

(1 citation statement)

References 15 publications

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“…Note. This also explains the fact that a space X admits a nearness iff it is symmetric (see Herrlich's paper [6]) while a frame L admits a (generalized) nearness iff it is subfit ( [7], see also [13]).…”

Section: Theorem a Space Is Subfit If And Only If For Each X ∈ X Andmentioning

confidence: 89%

New Aspects of Subfitness in Frames and Spaces

Picado

Pultr

2016

Appl Categor Struct

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This paper contains some new facts about subfitness and weak subfitness. In the case of spaces, subfitness is compared with the axiom of symmetry, and certain seeming discrepancies are explained. Further, Isbell's spatiality theorem in fact concerns a stronger form of spatiality (T1-spatiality) which is compared with the TD-spatiality. Then, a frame is shown to be subfit iff it contains no non-trivial replete sublocale, and the relation of repleteness and subfitness is also discussed in spaces. Another necessary and sufficient condition for subfitness presented is the validity of the meet formula for the Heyting operation, which was so far known only under much stronger conditions.

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Section: Theorem a Space Is Subfit If And Only If For Each X ∈ X Andmentioning

confidence: 89%

New Aspects of Subfitness in Frames and Spaces

Picado

Pultr

2016

Appl Categor Struct

Self Cite

View full text Add to dashboard Cite

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The assembly of a pointfree bispace and its two variations

Suarez

2022

Algebra Univers.

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More on Subfitness and Fitness

Picado

Pultr

2014

Appl Categor Struct

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The concepts of fitness and subfitness (as defined in Isbell [9]) are useful separation properties in point-free topology. The categorical behaviour of subfitness is bad and fitness is the closest modification that behaves well. The separation power of the two, however, differs very substantially and subfitness is transparent and turns out to be useful in its own right. Sort of supplementing the article [20] we present several facts on these concepts and their relation. First the "supportive" role subfitness plays when added to other properties is emphasized. In particular we prove that the numerous Dowker-Strauss type Hausdorff axioms become one for subfit frames. The aspects of fitness as a hereditary subfitness are analyzed, and a simple proof of coreflectivity of fitness is presented. Further, another property, prefitness, is shown to also produce fitness by heredity, in this case in a way usable for classical spaces, which results in a transparent characteristics of fit spaces. Finally, the properties are proved to be independent.

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(Sub)fit biframes and non-symmetric nearness

Cited by 6 publications

References 15 publications

New Aspects of Subfitness in Frames and Spaces

New Aspects of Subfitness in Frames and Spaces

The assembly of a pointfree bispace and its two variations

More on Subfitness and Fitness

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