scholarly journals (O-C)-compact Spaces and Hyperspaces Functor

2019 ◽  
Vol 5 (4) ◽  
pp. 30-37
Author(s):  
D. Jumaev
Keyword(s):  
Tychonoff Space ◽  
Compact Spaces ◽  
Nonempty Compact ◽  
Compact Subsets

In the work, it is established that the space of all nonempty compact subsets of a Tychonoff space is (O-C)–compact if and only if the give Tychonoff space is (O-C)–compact. Further, for a map f:X→Y the map expβX→Y is (O-C)–compact if and only if the map f is (O-C)–compact.

scholarly journals Li-Yorke Sensitivity of Set-Valued Discrete Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Heng Liu ◽  
Fengchun Lei ◽  
Lidong Wang
Keyword(s):  
Metric Space ◽  
Short Proof ◽  
Hausdorff Metric ◽  
Discrete Systems ◽  
Compact Metric Space ◽  
Continuous Map ◽  
Nonempty Compact ◽  
Compact Subsets

Consider the surjective, continuous mapf:X→Xand the continuous mapf¯of𝒦(X)induced byf, whereXis a compact metric space and𝒦(X)is the space of all nonempty compact subsets ofXendowed with the Hausdorff metric. In this paper, we give a short proof that iff¯is Li-Yoke sensitive, thenfis Li-Yorke sensitive. Furthermore, we give an example showing that Li-Yorke sensitivity offdoes not imply Li-Yorke sensitivity off¯.

scholarly journals Topologies on Superspaces of TVS-Cone Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xun Ge ◽  
Shou Lin
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Vietoris Topology ◽  
Cone Metric Spaces ◽  
Nonempty Compact ◽  
Cone Metric ◽  
Compact Subsets

This paper investigates superspaces𝒫0(X)and𝒦0(X)of a tvs-cone metric space(X,d), where𝒫0(X)and𝒦0(X)are the space consisting of nonempty subsets ofXand the space consisting of nonempty compact subsets ofX, respectively. The purpose of this paper is to establish some relationships between the lower topology and the lower tvs-cone hemimetric topology (resp., the upper topology and the upper tvs-cone hemimetric topology to the Vietoris topology and the Hausdorff tvs-cone hemimetric topology) on𝒫0(X)and𝒦0(X), which makes it possible to generalize some results of superspaces from metric spaces to tvs-cone metric spaces.

scholarly journals A note on compact sets in spaces of subsets

1988 ◽  
Vol 38 (3) ◽  
pp. 393-395 ◽  
Author(s):  
Phil Diamond ◽  
Peter Kloeden
Keyword(s):  
Metric Space ◽  
Complete Metric Space ◽  
Hausdorff Metric ◽  
Compact Sets ◽  
Selection Theorem ◽  
Starshaped Sets ◽  
Nonempty Compact ◽  
Compact Subsets

A simple characterisation is given of compact sets of the space K(X), of nonempty compact subsets of a complete metric space X, with the Hausdorff metric dH. It is used to give a new proof of the Blaschke selection theorem for compact starshaped sets.

scholarly journals Weakly m-compact via a hereditary class

2021 ◽  
Vol 39 (3) ◽  
pp. 123-135
Author(s):  
Abdo Qahis ◽  
Heyam Hussain AlJarrah ◽  
Takashi Noiri
Keyword(s):  
Topological Spaces ◽  
Compact Spaces ◽  
Hereditary Class ◽  
Compact Subsets

The aim of this paper is to introduce and study some types of m-compactness with respect to a hereditary class called weakly mH-compact spaces and weakly mH-compact subsets. We will provide several characterizations of weakly mH-compact spaces and investigate their relationships with some other classes of generalized topological spaces.

scholarly journals Applications on operations on weakly compact generalized topological spaces

2020 ◽  
Vol 12 (2) ◽  
pp. 461-467
Author(s):  
B. Roy ◽  
T. Noiri
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Weakly Compact ◽  
Compact Spaces ◽  
Generalized Topological Space ◽  
Compact Subsets

In this paper, we have introduced the notion of operations on a generalized topological space $(X,\mu)$ to investigate the notion of $\gamma_{_\mu}$-compact subsets of a generalized topological space and to study some of its properties. It is also shown that, under some conditions, $\gamma_{_\mu}$-compactness of a space is equivalent to some other weak forms of compactness. Characterizations of such sets are given. We have then introduced the concept of $\gamma_{_\mu}$-$T_{_2}$ spaces to study some properties of $\gamma_{_\mu}$-compact spaces. This operation enables us to unify different results due to S. Kasahara.

scholarly journals Volterra spaces revisited

2005 ◽  
Vol 79 (1) ◽  
pp. 61-76 ◽  
Author(s):  
Jiling Cao ◽  
David Gauld
Keyword(s):  
Homogeneous Space ◽  
Vietoris Topology ◽  
Topological Properties ◽  
Category Theorem ◽  
Nonempty Compact ◽  
Compact Subsets

AbstractIn this paper, we investigate Volterra spaces and relevant topological properties. New characterizations of weakly Volterra spaces are provided. An analogy of the Banach category theorem in terms of Volterra properties is obtained. It is shown that every weakly Volterra homogeneous space is Volterra, and there are metrizable Baire spaces whose hyperspaces of nonempty compact subsets endowed with the Vietoris topology are not weakly Volterra.

scholarly journals Vietoris topology on spaces dominated by second countable ones

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Carlos Islas ◽  
Daniel Jardon
Keyword(s):  
Compact Space ◽  
Discrete Space ◽  
Vietoris Topology ◽  
The Family ◽  
Nonempty Compact ◽  
The One ◽  
Eberlein Compact ◽  
One Point Compactification ◽  
Compact Subsets

AbstractFor a given space X let C(X) be the family of all compact subsets of X. A space X is dominated by a space M if X has an M-ordered compact cover, this means that there exists a family F = {FK : K ∈ C(M)} ⊂ C(X) such that ∪ F = X and K ⊂ L implies that FK ⊂ FL for any K;L ∈ C(M). A space X is strongly dominated by a space M if there exists an M-ordered compact cover F such that for any compact K ⊂ X there is F ∈ F such that K ⊂ F . Let K(X) D C(X)\{Ø} be the set of all nonempty compact subsets of a space X endowed with the Vietoris topology. We prove that a space X is strongly dominated by a space M if and only if K(X) is strongly dominated by M and an example is given of a σ-compact space X such that K(X) is not Lindelöf†. It is stablished that if the weight of a scattered compact space X is not less than c, then the spaces Cp(K(X)) and K(Cp(X)) are not Lindelöf Σ. We show that if X is the one-point compactification of a discrete space, then the hyperspace K(X) is semi-Eberlein compact.

scholarly journals Generalized fuzzy GV-Hausdorff distance in GFGV-fractal spaces with application in integral equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Alireza Alihajimohammad ◽  
Reza Saadati
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Hausdorff Distance ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric ◽  
Nonempty Compact ◽  
Compact Subsets

AbstractWe propose a method for constructing a generalized fuzzy Hausdorff distance on the set of the nonempty compact subsets of a given generalized fuzzy metric space in the sence of George–Veeramni and Tian–Ha–Tian. Next, we define the generalized fuzzy fractal spaces. Morever, we obtain a fixed point theorem of a class of generalized fuzzy contractions and present an application in integranl equation.

scholarly journals Upper semi continuity of attractors of delay differential equations in the delay

2006 ◽  
Vol 73 (2) ◽  
pp. 299-306 ◽  
Author(s):  
Peter E. Kloeden
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Global Attractor ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
Nonzero Constant ◽  
Nonempty Compact ◽  
Delay Differential ◽  
Compact Subsets

It is shown that if a retarded delay differential equation has a global attractor in the space C ([—τ0, ], ℝd) for a given nonzero constant delay τ0, then the equation has an attractor Aτ in the space C ([—τ, 0], ℝd) for nearby constant delays τ. Moreover the attractors Aτ converge upper semi continuously to in C ([—τ0, 0], ℝd) in the sense that they are identified through corresponding segments of entire trajectories in ℝd with nonempty compact subsets of C ([—τ0, 0], ℝd) which converge upper semi continuously to in C ([—τ0, 0], ℝd).

Some Constructions in Abstract Measure Theory

1975 ◽  
Vol 27 (4) ◽  
pp. 860-866 ◽  
Author(s):  
D. J. Lutzer
Keyword(s):  
Compact Subset ◽  
Measure Theory ◽  
Locally Compact ◽  
Compact Spaces ◽  
The Family ◽  
Abstract Measure ◽  
Locally Compact Spaces ◽  
Compact Subsets

In this paper we construct two examples which elucidate the relationships between several σ-algebras that arise in measure-theoretic constructions on locally compact spaces and groups. For any space X let (X) be the Borelσ-algebra on X, i.e., the smallest σ-algebra of subsets of X which contains the family of all closed subsets of X. Let δ (X) be the smallest δ-ring of subsets of X which contains every compact subset of X, where by a δ-ring we mean a collection of subsets of X which is closed under the formation of countable intersections, finite unions and relative complements. Let σ(X) be the smallest σ-ring of subsets of X which contains all compact subsets of X, where by a σ-ring we mean a collection of subsets of X which is closed under the formation of countable unions, finite intersections and relative complements.

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