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The Doitchinov Completion of a Regular Paratopological Group

Künzi, Hans-PeterRomaguera, SalvadorSipacheva, Ol’ga — 1998

Serdica Mathematical Journal

In memory of Professor D. Doitchinov ∗ This paper was written while the first author was supported by the Swiss National Science Foundation under grants 21–30585.91 and 2000-041745.94/1 and by the Spanish Ministry of Education and Sciences under DGES grant SAB94-0120. The second author was supported under DGES grant PB95-0737. During her stay at the University of Berne the third author was supported by the first author’s grant 2000-041745.94/1 from the Swiss National Science Foundation. ...

Approximate quantities, hyperspaces and metric completeness

Valentín GregoriSalvador Romaguera — 2000

Bollettino dell'Unione Matematica Italiana

Mostriamo che se X , d è uno spazio metrico completo, allora è completa anche la metrica D , indotta in modo naturale da d sul sottospazio degli insiemi sfocati («fuzzy») di X dati dalle quantità approssimate. Come è ben noto, D è una metrica molto interessante nella teoria dei punti fissi di applicazioni sfocate, poiché permette di ottenere risultati soddisfacenti in questo contesto.

Pairwise monotonically normal spaces

Josefa MarínSalvador Romaguera — 1991

Commentationes Mathematicae Universitatis Carolinae

We introduce and study the notion of pairwise monotonically normal space as a bitopological extension of the monotonically normal spaces of Heath, Lutzer and Zenor. In particular, we characterize those spaces by using a mixed condition of insertion and extension of real-valued functions. This result generalizes, at the same time improves, a well-known theorem of Heath, Lutzer and Zenor. We also obtain some solutions to the quasi-metrization problem in terms of the pairwise monotone normality.

On half-completion and bicompletion of quasi-metric spaces

Elena AlemanySalvador Romaguera — 1996

Commentationes Mathematicae Universitatis Carolinae

We characterize the quasi-metric spaces which have a quasi-metric half-completion and deduce that each paracompact co-stable quasi-metric space having a quasi-metric half-completion is metrizable. We also characterize the quasi-metric spaces whose bicompletion is quasi-metric and it is shown that the bicompletion of each quasi-metric compatible with a quasi-metrizable space X is quasi-metric if and only if X is finite.

Fixed points for cyclic orbital generalized contractions on complete metric spaces

Erdal KarapınarSalvador RomagueraKenan Taş — 2013

Open Mathematics

We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303]. Our results generalize some...

Weakly complete semimetrizable spaces and complete metrizability.

Salvador RomagueraSam D. Shore — 1996

Extracta Mathematicae

In [4], J. Ceder proved that every paracompact strongly complete semimetrizable space is completely metrizable. This result cannot be generalized to paracompact weakly complete semimetrizable spaces as a known example of L. F. McAuley shows (see [11, Theorem 3.2]). It then arises, in a natural way, the question of obtaining conditions for the complete metrizability of a paracompact weakly complete semimetrizable space. In this note we give an answer to this question. We show that every regular theta,...

Computing complexity distances between algorithms

We introduce a new (extended) quasi-metric on the so-called dual p-complexity space, which is suitable to give a quantitative measure of the improvement in complexity obtained when a complexity function is replaced by a more efficient complexity function on all inputs, and show that this distance function has the advantage of possessing rich topological and quasi-metric properties. In particular, its induced topology is Hausdorff and completely regular. Our approach is applied to the measurement...

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