Applied General Topology - Vol 05, No 1 (2004)
https://riunet.upv.es:443/handle/10251/82540
2024-06-21T04:01:59ZFuzzy quasi-metric spaces
https://riunet.upv.es:443/handle/10251/82552
Fuzzy quasi-metric spaces
Gregori, Valentín; Romaguera, Salvador
[EN] We generalize the notions of fuzzy metric by Kramosil and Michalek, and by George and Veeramani to the quasi-metric setting.We show that every quasi-metric induces a fuzzy quasi-metric and ,conversely, every fuzzy quasi-metric space generates a quasi-metrizable topology. Other basic properties are discussed.
2017-06-08T07:02:56ZPartial metrizability in value quantales
https://riunet.upv.es:443/handle/10251/82551
Partial metrizability in value quantales
Kopperman, Ralph D.; Matthews, S.; Pajoohesh, H.
[EN] Partial metrics are metrics except that the distance from a point to itself need not be 0. These are useful in modelling partially defined information, which often appears in computer science. We generalize this notion to study “partial metrics” whose values lie in a value quantale which may be other than the reals. Then each topology arises from such a generalized metric, and for each continuous poset, there is such a generalized metric whose topology is the Scott topology, and whose dual topology is the lower topology. These are both corollaries to our result that a bitopological space is pairwise completely regular if and only if there is such a generalized metric whose topology is the first topology, and whose dual topology is the second.
2017-06-08T07:00:56ZContinuous functions with compact support
https://riunet.upv.es:443/handle/10251/82550
Continuous functions with compact support
Acharyya, Sudip Kumar; Chattopadhyaya, K.C.; Ghosh, Partha Pratim
[EN] The main aim of this paper is to investigate a subring of the ring of continuous functions on a topological space X with values in a linearly ordered field F equipped with its order topology, namely the ring of continuous functions with compact support. Unless X is compact, these rings are commutative rings without unity. However, unlike many other commutative rings without unity, these rings turn out to have some nice properties, essentially in determining the property of X being locally compact non-compact or the property of X being nowhere locally compact. Also, one can associate with these rings a topological space resembling the structure space of a commutative ring with unity, such that the classical Banach Stone Theorem can be generalized to the case when the range field is that of the reals.
2017-06-08T06:58:29ZA countably compact free Abelian group whose size has countable cofinality
https://riunet.upv.es:443/handle/10251/82549
A countably compact free Abelian group whose size has countable cofinality
Castro Pereira, I.; Tomita, A.H.
[EN] Based on some set-theoretical observations, compactness results are given for general hit-and-miss hyperspaces. Compactness here is sometimes viewed splitting into “k-Lindelöfness” and ”k-compactness” for cardinals k. To focus only hit-and-miss structures, could look quite old-fashioned, but some importance, at least for the techniques, is given by a recent result of Som Naimpally, to who this article is hearty dedicated.
2017-06-08T06:56:07ZHomeomorphisms of R and the Davey Space
https://riunet.upv.es:443/handle/10251/82548
Homeomorphisms of R and the Davey Space
Carter, Sheila; Craveiro de Carvalho, F.J.
[EN] Up to homeomorphism, there are 9 topologies on a three point set {a, b, c}. Among the resulting topological spaces we have the so called Davey space, where the only non-trivial open set is, let us say, {a}. This is an interesting topological space to the extent that every topological space can be embedded in a product of Davey spaces. In this note we will consider the problem of obtaining the Davey space as a quotient R/G, where G is a suitable homeomorphism group. The present work can be regarded as a follow-up to some previous work done by one of the authors and Bernd Wegner.
2017-06-08T06:54:05ZStar-Hurewicz and related properties
https://riunet.upv.es:443/handle/10251/82547
Star-Hurewicz and related properties
Bonanzinga, M.; Cammaroto, F.; Kocinac, Ljubisa D.R.
[EN] We continue the investigation of star selection principles first considered. We are concentrated onto star versions of the Hurewicz covering property and star selection principles related to the classes of open covers which have been recently introduced.
2017-06-08T06:52:12ZSome problems on selections for hyperspace topologies
https://riunet.upv.es:443/handle/10251/82546
Some problems on selections for hyperspace topologies
Gutev, Valentin; Nogura, Tsugunori
[EN] The theory of hyperspaces has attracted the attention of many mathematicians who have found a large variety of its applications during the last decades. The theory has taken also its natural course and has yielded lots of problems which, besides their independent inner beauty, provide ties with numerous classical fields of mathematics. In the present note we are concerned with some open problems about selections for hyperspace topologies which have been in the scope of our recent research interests.
2017-06-08T06:49:42ZA topological approach to Best Approximation Theory
https://riunet.upv.es:443/handle/10251/82545
A topological approach to Best Approximation Theory
Moreno, Samuel G.; Almira, Jose María; García-Caballero, Esther M.; Quesada, J.M.
[EN] The main goal of this paper is to put some light in several arguments that have been used through the time in many contexts of Best Approximation Theory to produce proximinality results. In all these works, the main idea was to prove that the sets we are considering have certain properties which are very near to the compactness in the usual sense. In the paper we introduce a concept (the wrapping) that allow us to unify all these results in a whole theory, where certain ideas from Topology are essential. Moreover, we do not only cover many of the known classical results but also prove some new results. Hence we prove that exists a strong interaction between General Topology and Best Approximation Theory.
2017-06-08T06:47:19ZThe topological structure of (homogeneous) spaces and groups with countable cs∗-character
https://riunet.upv.es:443/handle/10251/82544
The topological structure of (homogeneous) spaces and groups with countable cs∗-character
Banak, Taras; Zdomskyi, Lubomyr
[EN] In this paper we introduce and study three new cardinal topological invariants called the cs∗-, cs-, and sb-characters. The class of topological spaces with countable cs∗-character is closed under many topological operations and contains all N-spaces and all spaces with point-countable cs∗-network. Our principal result states that each non-metrizable sequential topological group with countable cs∗- character has countable pseudo-character and contains an open kω- subgroup. This result is specific for topological groups: under Martin Axiom there exists a sequential topologically homogeneous kω-space X with N0 = cs∗x (X) <ψ (X).
2017-06-08T06:44:30ZRepresentations of ordered semigroups and the Physical concept of Entropy
https://riunet.upv.es:443/handle/10251/82543
Representations of ordered semigroups and the Physical concept of Entropy
Candeal, Juan C.; de Miguel, Juan R.; Induráin, Esteban; Mehta, Ghansyam B.
[EN] The abstract concept of entropy is interpreted throughthe concept of numerical representation of a totally preordered set sothat the concept of composition of systems or additivity of entropy canbe analyzed through the study of additive representations of totallyordered semigroups
2017-06-08T06:41:51Z