Property (G), Regularity, and Semi-Equicontinuity

1973 ◽  
Vol 16 (4) ◽  
pp. 587-594
Author(s):  
J. S. Yang
Keyword(s):  
Topological Group ◽  
Function Spaces ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Semitopological Group ◽  
Function Of Two Variables ◽  
The Way

This note, motivated by [2], [3], and [4], is devoted to an investigation of properties related to equicontinuity in function spaces of topological spaces. In §2, we study the property (G) defined in [3], and the regularity defined in [4]. A sufficient condition for the simultaneous continuity of a function of two variables, which is analogous to a well known result in equicontinuity, is given at the end of the section. In §3, we relate the regularity with the semi-equicontinuity defined in [2], by localizing the semi-equicontinuity in an obvious way which leads us to weaken some of the hypotheses used in [2]. By the way of constructing an example, we also obtained a sufficient condition for a regular semitopological group to be a topological group.

scholarly journals ‎INSERTION OF A CONTRA-CONTINUOUS FUNCTION BETWEEN TWO ‎‎COMPARABLE CONTRA-$\alpha-$CONTINUOUS (CONTRA-$C-$CONTINUOUS) FUNCTIONS

2019 ◽  
pp. 13
Author(s):  
Majid Mirmiran ◽  
Binesh Naderi
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

‎A necessary and sufficient condition in terms of lower cut sets ‎are given for the insertion of a contra-continuous function ‎between two comparable real-valued functions on such topological ‎spaces that kernel of sets are open‎. 

Criteria of Personal Identity

1975 ◽  
Vol 7 (1) ◽  
pp. 47-69
Author(s):  
Karl Ameriks
Keyword(s):  
Personal Identity ◽  
Primary Objective ◽  
Psychological Characteristics ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Bodily Continuity ◽  
Secondary Objective ◽  
The Way

The primary objective of this paper is to improve the defense of the thesis that(1) bodily continuity is the primary criterion of personal identity.This is to be done by establishing (in Parts Ill and IV) that there is a unique sense in which(2) bodily continuity is a necessary condition of personal identity.A secondary objective of the paper is to illustrate (in Part I) the way in which the value and validity of (2) has been obscured in recent defenses and criticisms of (1), which inappropriately interpret it in terms of the claim that(3) bodily continuity is a sufficient condition of personal identity.Since the truth of (3) will be denied, the defense of (1) will also involve arguing (in Part II) that the traditional alternative to the bodily criterion, namely the criterion of memory and psychological characteristics, not only is not a necessary condition of personal identity but also is not a sufficient condition.

On the size of quotients of function spaces on a topological group

2011 ◽  
Vol 202 (3) ◽  
pp. 243-259 ◽  
Author(s):  
Ahmed Bouziad ◽  
Mahmoud Filali
Keyword(s):  
Topological Group ◽  
Function Spaces

Triangulating Topological Spaces

1997 ◽  
Vol 07 (04) ◽  
pp. 365-378 ◽  
Author(s):  
Herbert Edelsbrunner ◽  
Nimish R. Shah
Keyword(s):  
Homotopy Equivalent ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Voronoi Cells ◽  
Delaunay Complex ◽  
Common Intersection ◽  
Finite Set ◽  
The Common ◽  
Nerve Theorem

Given a subspace [Formula: see text] and a finite set S⊆ℝd, we introduce the Delaunay complex, [Formula: see text], restricted by [Formula: see text]. Its simplices are spanned by subsets T⊆S for which the common intersection of Voronoi cells meets [Formula: see text] in a non-empty set. By the nerve theorem, [Formula: see text] and [Formula: see text] are homotopy equivalent if all such sets are contractible. This paper proves a sufficient condition for [Formula: see text] and [Formula: see text] be homeomorphic.

scholarly journals Metrisation of Moore spaces and abstract topological manifolds

1997 ◽  
Vol 56 (3) ◽  
pp. 395-401 ◽  
Author(s):  
David L. Fearnley
Keyword(s):  
Recent Work ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Moore Space ◽  
Global Coherence ◽  
Topological Manifolds ◽  
Necessary And Sufficient ◽  
Moore Spaces ◽  
Significant Class

The problem of metrising abstract topological spaces constitutes one of the major themes of topology. Since, for each new significant class of topological spaces this question arises, the problem is always current. One of the famous metrisation problems is the Normal Moore Space Conjecture. It is known from relatively recent work that one must add special conditions in order to be able to get affirmative results for this problem. In this paper we establish such special conditions. Since these conditions are characterised by local simplicity and global coherence they are referred to in this paper generically as “abstract topological manifolds.” In particular we establish a generalisation of a classical development of Bing, giving a proof which is complete in itself, not depending on the result or arguments of Bing. In addition we show that the spaces recently developed by Collins designated as “W satisfying open G(N)” are metrisable if they are locally separable and locally connected and regular. Finally, we establish a new necessary and sufficient condition for spaces to be metrisable.

scholarly journals Positive operators and approximation in function spaces on completely regular spaces

2003 ◽  
Vol 2003 (61) ◽  
pp. 3841-3871 ◽  
Author(s):  
Francesco Altomare ◽  
Sabrina Diomede
Keyword(s):  
Natural Extension ◽  
Function Spaces ◽  
Positive Operators ◽  
Linear Operators ◽  
Topological Spaces ◽  
Approximation Properties ◽  
Completely Regular ◽  
Borel Measures ◽  
Korovkin Type Theorems ◽  
Locally Convex

We discuss the approximation properties of nets of positive linear operators acting on function spaces defined on Hausdorff completely regular spaces. A particular attention is devoted to positive operators which are defined in terms of integrals with respect to a given family of Borel measures. We present several applications which, in particular, show the advantages of such a general approach. Among other things, some new Korovkin-type theorems on function spaces on arbitrary topological spaces are obtained. Finally, a natural extension of the so-called Bernstein-Schnabl operators for convex (not necessarily compact) subsets of a locally convex space is presented as well.

scholarly journals A NECESSARY AND SUFFICIENT CONDITION FOR CERTAIN MARTINGALE INEQUALITIES IN BANACH FUNCTION SPACES

2007 ◽  
Vol 49 (3) ◽  
pp. 431-447 ◽  
Author(s):  
MASATO KIKUCHI
Keyword(s):  
Function Space ◽  
Probability Space ◽  
Banach Function Space ◽  
Sufficient Conditions ◽  
Function Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Banach Function Spaces ◽  
Martingale Inequalities ◽  
Necessary And Sufficient

AbstractLet X be a Banach function space over a nonatomic probability space. We investigate certain martingale inequalities in X that generalize those studied by A. M. Garsia. We give necessary and sufficient conditions on X for the inequalities to be valid.

scholarly journals A study of some aspects of topological groups

Filomat ◽  
2007 ◽  
Vol 21 (1) ◽  
pp. 55-65
Author(s):  
M.R. Adhikari ◽  
M. Rahaman
Keyword(s):  
Topological Group ◽  
Group Structure ◽  
Base Point ◽  
Homotopy Category ◽  
Topological Spaces ◽  
Topological Groups ◽  
Homotopy Classes ◽  
Continuous Maps

The aim of this paper is to find a generalization of topological groups. The concept arises out of the investigation to obtain a group structure on the set [X,Y], of homotopy classes of maps from a space X to a given space Y for all X which is natural with respect to X. We also study the generalized topological groups. Finally, associated with each generalized topological group we construct a contra variant functor from the homotopy category of pointed topological spaces and base point preserving continuous maps to the category of groups and homomorphism.

scholarly journals Von Staatsgrenze zu Dialektgrenze.

2019 ◽  
Vol 98 (5) ◽  
pp. 307-328
Author(s):  
Pascale Erhart
Keyword(s):  
The Political ◽  
Sufficient Condition ◽  
Current State ◽  
Political Border ◽  
National Border ◽  
Project Data ◽  
The University ◽  
Upper Rhine ◽  
Cultural Features ◽  
The Way

The ANR/DFG cooperation project called “FLARS – Effects of the national border on the linguistic situation in the Upper Rhine area”, between the University of Freiburg and the University of Strasbourg, examined the emergence and the nature of a linguistic border between France and Germany in the Alemannic-speaking regions Alsace and Baden, and its interdependence with the political border. The project data were collected through interviews conducted in 40 localities alongside the political border. The questions focused on what informants think and say about languages and about their use of them; about the current state of the dialects, the way they are spoken, their usefulness, their importance; and also on what they think and say about the way the inhabitants of the other side of the Rhine speak, what may make it different, and their position regarding that. A first analysis shows that most of the French and German informants think that both sides of the Rhine do not differ much linguistically, but that this proximity is not a sufficient condition for evoking a “transnational language”, as other aspects of their lives, lifestyles and identities are considered as different. This article will focus on the discourse produced by dialect speakers about the Rhine as a border and about common or different linguistic and cultural features with their neighbours.

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