Applied General Topology - Vol 06, No 2 (2005)https://riunet.upv.es:443/handle/10251/826032024-07-14T19:43:47Z2024-07-14T19:43:47ZOn Banach fixed point theorems for partial metric spacesValero, Oscarhttps://riunet.upv.es:443/handle/10251/826362023-11-21T11:47:18Z2017-06-09T08:45:24ZOn Banach fixed point theorems for partial metric spaces
Valero, Oscar
[EN] In this paper we prove several generalizations of the Banach fixed point theorem for partial metric spaces (in the sense of O’Neill) given in, obtaining as a particular case of our results the Banach fixed point theorem of Matthews ([12]), and some well-known classical fixed point theorems when the partial metric is, in fact, a metric.
2017-06-09T08:45:24ZOn semi-Lipschitz functions with values in a quasi-normed linear spaceSánchez-Álvarez, José Manuelhttps://riunet.upv.es:443/handle/10251/826352023-11-21T11:47:18Z2017-06-09T08:43:23ZOn semi-Lipschitz functions with values in a quasi-normed linear space
Sánchez-Álvarez, José Manuel
[EN] In a recent paper, S. Romaguera and M. Sanchis discussed several properties of semi-Lipschitz real valued functions. In this paper we analyze the structure of the space of semi-Lipschitz functions that are valued in a quasi-normed linear space. Our approach is motivated, in part, by the fact that this structure can be applied to study some processes in the theory of complexity spaces.
2017-06-09T08:43:23ZTi-ordered reflectionsKünzi, Hans-Peter A.Richmond, Thomas A.https://riunet.upv.es:443/handle/10251/826342023-11-21T11:47:19Z2017-06-09T08:39:51ZTi-ordered reflections
Künzi, Hans-Peter A.; Richmond, Thomas A.
[EN] We present a construction which shows that the Ti-ordered reflection (i ϵ {0, 1, 2}) of a partially ordered topological space (X, , τ, ≤) exists and is an ordered quotient of (X, τ, ≤). We give an explicit construction of the T0-ordered reflection of an ordered topological space (X, τ, ≤), and characterize ordered topological spaces whose T0-ordered reflection is T1-ordered.
2017-06-09T08:39:51ZThe canonical partial metric and the uniform convexity on normed spacesOltra, S.Romaguera, SalvadorSánchez-Pérez, E.A.https://riunet.upv.es:443/handle/10251/826332023-11-21T11:47:19Z2017-06-09T08:36:19ZThe canonical partial metric and the uniform convexity on normed spaces
Oltra, S.; Romaguera, Salvador; Sánchez-Pérez, E.A.
[EN] In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm.
We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space.
2017-06-09T08:36:19ZA note on locally v-bounded spacesGeorgiou, D.N.Iliadis, S.D.https://riunet.upv.es:443/handle/10251/826322023-11-21T11:47:18Z2017-06-09T08:32:50ZA note on locally v-bounded spaces
Georgiou, D.N.; Iliadis, S.D.
[EN] In this paper, on the family O(Y ) of all open subsets of a space Y (actually on a complete lattice) we define the so called strong v-Scott topology, denoted by τ8v, where v is an infinite cardinal. This topology defines on the set C(Y,Z) of all continuous functions on the space Y to a space Z a topology τ8v. The topology τ8v, is always larger than or equal to the strong Isbell topology. We study the topology τ8v in the case where Y is a locally v-bounded space.
2017-06-09T08:32:50ZCompactness properties of bounded subsets of spaces of vector measure integrable functions and factorization of operatorsGarcia-Raffi, L. M.Sánchez-Pérez, E.A.https://riunet.upv.es:443/handle/10251/826312023-11-21T11:47:18Z2017-06-09T08:30:49ZCompactness properties of bounded subsets of spaces of vector measure integrable functions and factorization of operators
Garcia-Raffi, L. M.; Sánchez-Pérez, E.A.
[EN] Using compactness properties of bounded subsets of spaces of vector measure integrable functions and a representation theorem for q-convex Banach lattices, we prove a domination theorem for operators between Banach lattices. We generalize in this way several classical factorization results for operators between these spaces, as psumming operators.
2017-06-09T08:30:49ZOn some applications of fuzzy pointsGanster, MaximilianGeorgiou, D.N.Jafari, S.Moshokoa, S.P.https://riunet.upv.es:443/handle/10251/826302023-11-21T11:47:19Z2017-06-09T08:26:45ZOn some applications of fuzzy points
Ganster, Maximilian; Georgiou, D.N.; Jafari, S.; Moshokoa, S.P.
[EN] The notion of preopen sets play a very important role in General Topology and Fuzzy Topology. Preopen sets are also called nearly open and locally dense. The purpose of this paper is to give some applications of fuzzy points in fuzzy topological spaces. Moreover, in section 2 we offer some properties of fuzzy preclosed sets through the contribution of fuzzy points and we introduce new separation axioms in fuzzy topological spaces. Also using the notions of weak and strong fuzzy points, we investigate some properties related to the preclosure of such points, and also their impact on separation axioms. In section 3, using the notion of fuzzy points, we introduce and study the notions of fuzzy pre-upper limit, fuzzy pre-lower limit and fuzzy pre-limit. Finally in section 4, we introduce the fuzzy pre-continuous convergence on the set of fuzzy pre-continuous functions and give a characterization of the fuzzy pre-continuous convergence through the assistance of fuzzy pre-upper limit.
2017-06-09T08:26:45ZThe language of topology: a Turkish case studyBarton, BillLichtenberk, FrankReilly, Ivanhttps://riunet.upv.es:443/handle/10251/826292023-11-21T11:47:19Z2017-06-09T08:19:57ZThe language of topology: a Turkish case study
Barton, Bill; Lichtenberk, Frank; Reilly, Ivan
[EN] Topology has its own specialised language. Where did this come from? What are the differences in the language of topology when it is expressed in English, Spanish, Mandarin, Czech or Turkish? Does topology itself change when expressed in different languages? What effect has language had on the development of topology? Does the language of the topologist make a difference to the mathematics? A research programme aimed at answering these questions has begun. This paper is the first in a series that provides a background to the research. Topological discourse in various languages is being examined for its particular features, and possible influences on the concepts developed through these languages. Data from Turkish topologists and topological terminology are examined. They show why there is reason to suspect that language influences mathematical concept development. The data are also used to explore methodological issues for the research project.
2017-06-09T08:19:57Z