Semilattices of totally bounded quasi-uniformities

Künzi, Hans-Peter A.; Losonczi, Attila

doi:10.1016/s0166-8641(00)00048-1

Cited by 9 publications

(4 citation statements)

References 9 publications

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“…We conclude this section extending to our context the well-known and interesting result [10,22] that every totally bounded quiet quasi-uniform space is a uniform space.…”

Section: Proposition 3 a Fuzzy Quasi-metric Space (X M * ) Is Quiementioning

confidence: 58%

Quasi-uniform isomorphisms in fuzzy quasi-metric spaces, bicompletion and D-completion

2007

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V. Gregori and S. Romaguera [17] obtained an example of a fuzzy metric space (in the sense of A. George and P. Veeramani) that is not completable, i.e. it is not isometric to a dense subspace of any complete fuzzy metric space; therefore, and contrary to the classical case, there exist quiet fuzzy quasi-metric spaces that are not bicompletable neither D-completable, via (quasi-)isometries. In this paper we show that, nevertheless, it is possible to obtain solutions to the problem of completion of fuzzy quasi-metric spaces by using quasi-uniform isomorphisms instead of (quasi-)isometries. Such solutions are deduced from a general method, given here, to obtain extension properties of fuzzy quasi-metric spaces from the corresponding ones of the classical theory of quasi-uniform and quasi-metric spaces.

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“…We conclude this section extending to our context the well-known and interesting result [10,22] that every totally bounded quiet quasi-uniform space is a uniform space.…”

Section: Proposition 3 a Fuzzy Quasi-metric Space (X M * ) Is Quiementioning

confidence: 58%

Quasi-uniform isomorphisms in fuzzy quasi-metric spaces, bicompletion and D-completion

2007

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“…H.-P. Künzi and M. J. Pérez-Peñalver in [6] prove some interesting results about the number of quasi-proximities that a topological spaces admits. H.-P. Künzi in [3] studies the number of quasi-uniformities belonging to the Pervin quasi-proximity class.…”

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confidence: 91%

A note on unibasic spaces and transitive quasi-proximities

García-Máynez

Acosta

2017

Appl. Gen. Topol.

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“…Unfortunately, Doitchinov's condition of balancedness turns out to be rather restrictive. For instance, balanced 0 quasimetrics induce completely regular Hausdorff topologies (see [1,Corollary 3] and [8,Page 208]) and totally bounded balanced 0 quasimetrics induce uniformities (see [9,10]). Künzi and Kivuvu [11,12] localize Doitchinov's idea of balancedness; that is, they do not work with arbitrary Cauchy filter pairs but only with those that they call balanced Cauchy filter pairs.…”

Section: Introductionmentioning

confidence: 99%

A Solution to the Completion Problem for Quasi-Pseudometric Spaces

Andrikopoulos

2013

International Journal of Mathematics and Mathematical Sciences

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The different notions of Cauchy sequence and completeness proposed in the literature for quasi-pseudometric spaces do not provide a satisfactory theory of completeness and completion for all quasi-pseudometric spaces. In this paper, we introduce a notion of completeness which is classical in the sense that it is made up of equivalence classes of Cauchy sequences and constructs a completion for any given 0 quasi-pseudometric space. This new completion theory extends the existing completion theory for metric spaces and satisfies the requirements posed by Doitchinov for a nice theory of completeness.

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Semilattices of totally bounded quasi-uniformities

Cited by 9 publications

References 9 publications

Quasi-uniform isomorphisms in fuzzy quasi-metric spaces, bicompletion and D-completion

Quasi-uniform isomorphisms in fuzzy quasi-metric spaces, bicompletion and D-completion

A note on unibasic spaces and transitive quasi-proximities

A Solution to the Completion Problem for Quasi-Pseudometric Spaces

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