scholarly journals On âg Compact Spaces

2014 ◽  
Vol 10 ◽  
pp. 19-22
Author(s):  
V. Senthilkumaran ◽  
R. Krishnakumar ◽  
Y. Palaniappan
Keyword(s):  
Topological Space ◽  
Compact Sets ◽  
Compact Spaces

We introduce and study some subsets of a topological space X called âg compact sets; âg compact spaces are defined and their properties are studied.

Zero-Dimensional Compactifications of Locally Compact Spaces

1974 ◽  
Vol 26 (4) ◽  
pp. 920-930 ◽  
Author(s):  
R. Grant Woods
Keyword(s):  
Topological Space ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Dense Subspace ◽  
Locally Compact ◽  
Partially Order ◽  
Compact Spaces ◽  
Hausdorff Topological Space ◽  
Continuous Map ◽  
Locally Compact Spaces

Let X be a locally compact Hausdorff topological space. A compactification of X is a compact Hausdorff space which contains X as a dense subspace. Two compactifications αX and γX of X are equivalent if there is a homeomorphism from αX onto γX that fixes X pointwise. We shall identify equivalent compactifications of a given space. If is a family of compactifications of X, we can partially order by saying that αX ≦ γX if there is a continuous map from γX onto αX that fixes X pointwise.

scholarly journals rc-continuous functions and functions with rc-strongly closed graph

2003 ◽  
Vol 2003 (72) ◽  
pp. 4547-4555
Author(s):  
Bassam Al-Nashef
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Continuous Functions ◽  
Closed Graph ◽  
Compact Spaces ◽  
Extremally Disconnected ◽  
The Family ◽  
Regular Closed

The family of regular closed subsets of a topological space is used to introduce two concepts concerning a functionffrom a spaceXto a spaceY. The first of them is the notion offbeing rc-continuous. One of the established results states that a spaceYis extremally disconnected if and only if each continuous function from a spaceXtoYis rc-continuous. The second concept studied is the notion of a functionfhaving an rc-strongly closed graph. Also one of the established results characterizes rc-compact spaces (≡S-closed spaces) in terms of functions that possess rc-strongly closed graph.

A note on λ-compact spaces

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
O. Karamzadeh ◽  
M. Namdari ◽  
M. Siavoshi
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Compact Spaces

AbstractWe extend the well-known and important fact that “a topological space X is compact if and only if every ideal in C(X) is fixed”, to more general topological spaces. Some interesting consequences are also observed. In particular, the maximality of compact Hausdorff spaces with respect to the property of compactness is generalized and the topological spaces with this generalized property are characterized.

scholarly journals Compact and extremally disconnected spaces

2004 ◽  
Vol 2004 (20) ◽  
pp. 1047-1056
Author(s):  
Bhamini M. P. Nayar
Keyword(s):  
Topological Space ◽  
Compact Space ◽  
Closed Subset ◽  
Hausdorff Space ◽  
Hausdorff Spaces ◽  
Compact Spaces ◽  
Hausdorff Topological Space ◽  
Extremally Disconnected

Viglino defined a Hausdorff topological space to beC-compact if each closed subset of the space is anH-set in the sense of Veličko. In this paper, we study the class of Hausdorff spaces characterized by the property that each closed subset is anS-set in the sense of Dickman and Krystock. Such spaces are calledC-s-compact. Recently, the notion of strongly subclosed relation, introduced by Joseph, has been utilized to characterizeC-compact spaces as those with the property that each function from the space to a Hausdorff space with a strongly subclosed inverse is closed. Here, it is shown thatC-s-compact spaces are characterized by the property that each function from the space to a Hausdorff space with a strongly sub-semiclosed inverse is a closed function. It is established that this class of spaces is the same as the class of Hausdorff, compact, and extremally disconnected spaces. The class ofC-s-compact spaces is properly contained in the class ofC-compact spaces as well as in the class ofS-closed spaces of Thompson. In general, a compact space need not beC-s-compact. The product of twoC-s-compact spaces need not beC-s-compact.

scholarly journals On the Fuzzy Number Space with the Level Convergence Topology

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. J. Font ◽  
A. Miralles ◽  
M. Sanchis
Keyword(s):  
Topological Space ◽  
Fuzzy Number ◽  
Continuous Functions ◽  
Topological Properties ◽  
Compact Sets ◽  
Compact Open Topology ◽  
Locally Compact ◽  
Compact Topological Space ◽  
Convergence Topology

We characterize compact sets of𝔼1endowed with the level convergence topologyτℓ. We also describe the completion(𝔼1̂,𝒰̂)of𝔼1with respect to its natural uniformity, that is, the pointwise uniformity𝒰, and show other topological properties of𝔼1̂, as separability. We apply these results to give an Arzela-Ascoli theorem for the space of(𝔼1,τℓ)-valued continuous functions on a locally compact topological space equipped with the compact-open topology.

scholarly journals Continuous functions between sets with operations

2020 ◽  
Vol 24 (2) ◽  
pp. 225-239
Author(s):  
Fumie Nakaoka ◽  
Nobuyuki Oda
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Compact Spaces ◽  
Fundamental Properties ◽  
Connected Spaces

A set with an operation is a generalization of a topological space. Two types of continuous functions are dened between sets with operations. They are characterized making use of two types of closures and interiors. Homeomorphisms between sets with operations are also characterized. Variants of subspaces, connected spaces and compact spaces are introduced in a set with an operation and some fundamental properties of them are proved.

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 Generalized products of weakly m — n compact spaces, I

1982 ◽  
Vol 33 (2) ◽  
pp. 143-151 ◽  
Author(s):  
U. N. B. Dissanayake
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Open Cover ◽  
Compact Spaces

AbstractA topological space X is said to be weakly-Lindelöf if and only if every open cover of X has a countable sub-family with dense union. We know that products of two Lindelöf spaces need not be weakly-Lindelöf. In this paper we obtain non-trivial sufficient conditions on small sub-products to ensure the producitivity of the property weakly-Lindelöf with respect to arbitrary products.

scholarly journals Walrasian economy and some properties of convexly compact sets

2017 ◽  
Vol 25 (1) ◽  
pp. 69-76
Author(s):  
Mirela Cristea ◽  
Doina Dascălu ◽  
Laura Nicoleta Nasta
Keyword(s):  
Topological Space ◽  
Excess Demand ◽  
Compact Set ◽  
Compact Sets

AbstractG. Žitković defined the notion of a convexly compact set in a topological space and, among other things, used it to give an extension of the Walrasian excess-demand theorem. We continue the study of convexly compactness in LCS spaces and prove a Krein-Milman theorem in this setting.

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