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Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation

Dhagat, Vanita Ben, Sharma, Akshay (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 54H25, 47H10.The concept of semi compatibility is given in probabilistic metric space and it has been applied to prove the existence of unique common fixed point of four self-maps with weak compatibility satisfying an implicit relation. At the end we provide examples in support of the result.Authors thank to MPCOST, Bhopal for financial support through the project M-19/2006.

Weak continuity properties of topologized groups

J. Cao, R. Drozdowski, Zbigniew Piotrowski (2010)

Czechoslovak Mathematical Journal

We explore (weak) continuity properties of group operations. For this purpose, the Novak number and developability number are applied. It is shown that if ( G , · , τ ) is a regular right (left) semitopological group with dev ( G ) < Nov ( G ) such that all left (right) translations are feebly continuous, then ( G , · , τ ) is a topological group. This extends several results in literature.

Weak-bases and D -spaces

Dennis K. Burke (2007)

Commentationes Mathematicae Universitatis Carolinae

It is shown that certain weak-base structures on a topological space give a D -space. This solves the question by A.V. Arhangel’skii of when quotient images of metric spaces are D -spaces. A related result about symmetrizable spaces also answers a question of Arhangel’skii. Theorem.Any symmetrizable space X is a D -space ( hereditarily ) . Hence, quotient mappings, with compact fibers, from metric spaces have a D -space image. What about quotient s -mappings? Arhangel’skii and Buzyakova have shown that...

Weakly complete semimetrizable spaces and complete metrizability.

Salvador Romaguera, Sam 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,...

Weak-open compact images of metric spaces

Sheng Xiang Xia (2008)

Czechoslovak Mathematical Journal

The main results of this paper are that (1) a space X is g -developable if and only if it is a weak-open π image of a metric space, one consequence of the result being the correction of an error in the paper of Z. Li and S. Lin; (2) characterizations of weak-open compact images of metric spaces, which is another answer to a question in in the paper of Y. Ikeda, C. liu and Y. Tanaka.

Weil uniformities for frames

Jorge Picado (1995)

Commentationes Mathematicae Universitatis Carolinae

In pointfree topology, the notion of uniformity in the form of a system of covers was introduced by J. Isbell in [11], and later developed by A. Pultr in [14] and [15]. Another equivalent notion of locale uniformity was given by P. Fletcher and W. Hunsaker in [6], which they called “entourage uniformity”. The purpose of this paper is to formulate and investigate an alternative definition of entourage uniformity which is more likely to the Weil pointed entourage uniformity, since it is expressed...

When are Borel functions Baire functions?

M. Fosgerau (1993)

Fundamenta Mathematicae

The following two theorems give the flavour of what will be proved. Theorem. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0,1] to Y coincide if and only if Y is connected and locally connected.Theorem. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class functions from [0,1] to Y coincide if and only if for all finite sequences U 1 , . . . , U q of nonempty open subsets of Y there...

When C p ( X ) is domain representable

William Fleissner, Lynne Yengulalp (2013)

Fundamenta Mathematicae

Let M be a metrizable group. Let G be a dense subgroup of M X . We prove that if G is domain representable, then G = M X . The following corollaries answer open questions. If X is completely regular and C p ( X ) is domain representable, then X is discrete. If X is zero-dimensional, T₂, and C p ( X , ) is subcompact, then X is discrete.

When spectra of lattices of z -ideals are Stone-Čech compactifications

Themba Dube (2017)

Mathematica Bohemica

Let X be a completely regular Hausdorff space and, as usual, let C ( X ) denote the ring of real-valued continuous functions on X . The lattice of z -ideals of C ( X ) has been shown by Martínez and Zenk (2005) to be a frame. We show that the spectrum of this lattice is (homeomorphic to) β X precisely when X is a P -space. This we actually show to be true not only in spaces, but in locales as well. Recall that an ideal of a commutative ring is called a d -ideal if whenever two elements have the same annihilator and...

Whitney maps-a non-metric case

Janusz Charatonik, Włodzimierz Charatonik (2000)

Colloquium Mathematicae

It is shown that there is no Whitney map on the hyperspace 2 X for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).

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