Convergence

Bentley, H. L.; Herrlich, Horst; Lowen-Colebunders, E.

doi:10.1016/0022-4049(90)90130-a

Cited by 21 publications

(13 citation statements)

References 27 publications

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“…and because f ω ε := d ω ε (x, ·) ∈ AP((X, δ), R), we are done. That (2) implies (3) is clear since for every f ∈ AP((X, δ), R) and ω < ∞ , obviously |f | ∧ ω ∈ AP((X, δ), R). Finally we show that (3) implies (1).…”

Section: 4mentioning

confidence: 91%

“…We will now derive an explicit description for the epireflector from AP onto AP 2 , along the same lines as was done for the T 1 -case in the section above. First we define a property R for approach spaces, which is inspired by the notion of reciprocity for convergence spaces, as defined in [2].…”

Section: A(y)mentioning

confidence: 99%

“…We first show that (1) implies (2). Therefore let D be a collection of ∞p-metrics on X which is closed w.r.t.…”

mentioning

confidence: 99%

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A note on separation in AP

Löwen

Sioen²

2003

Appl. Gen. Topol.

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Dedicated to Professor S. Naimpally on the occasion of his 70 th birthday.Abstract. It is our aim in this note to take a closer look at some separation axioms in the construct AP of approach spaces and contractions. Whereas lower separation axioms seem to be qualitative, the higher ones seem to have a quantitative nature. Also some characterizations for the corresponding epireflectors will be given.2000 AMS Classification: 54A05, 54D10, 54D15, 54B30.

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Section: 4mentioning

confidence: 91%

Section: A(y)mentioning

confidence: 99%

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A note on separation in AP

Löwen

Sioen²

2003

Appl. Gen. Topol.

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“…In 1990, Bently et al [1] formalised the concept of filter spaces for being isomorphic to Katetov's [2] filter merotopic spaces. Since then these spaces have been studied by several topologists (see [3], [4], [5], [6], [7]) in the context of their applications to category theory and algebra .…”

Section: Introductionmentioning

confidence: 99%

Quasi-Completion of Filter Spaces

Rath¹

2015

Int. J. of Pure and Appl. Math.

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The category F IL of filter spaces being isomorphic to the category of grill-determined nearness spaces has become significant in the later part of the twentieth century. During that period, a substantial completion theory has been developed using the equivalence classes of filters in a filter space. However, that completion was quite general in nature, and did not allow the finest such completion. As a result, a completion functor could not be defined on F IL. In this paper, this issue is partially addressed by constructing a completion that is finer than the existing completions. Also, a completion functor is defined on a subcategory of F IL comprising all filter spaces as objects.

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“…If we exclude the last of three Keller's [22] axioms for a Cauchy space, then the resulting space is what we call a …lter space. In [15], it is shown that the category FIL of …lter spaces is isomorphic to the category of …lter meretopic spaces which were introduced by Katµ etov [21]. The category of Cauchy spaces is also known to be a bire ‡ective, …nally dense subcategory of FIL [35].…”

Section: Introductionmentioning

confidence: 99%