scholarly journals Intrinsic characterizations of C-realcompact spaces

2021 ◽  
Vol 22 (2) ◽  
pp. 295
Author(s):  
Sudip Kumar Acharyya ◽  
Rakesh Bharati ◽  
Atasi Deb Ray
Keyword(s):  
Topological Space ◽  
Dense Subspace ◽  
Finite Intersection ◽  
Compact Spaces ◽  
Closed Sets ◽  
Finite Intersection Property ◽  
Arbitrary Topological Space ◽  
Stable Family ◽  
Definition Of

<pre>c-realcompact spaces are introduced by Karamzadeh and Keshtkar in Quaest. Math. 41, no. 8 (2018), 1135-1167. We offer a characterization of these spaces X via c-stable family of closed sets in X by showing that  X is c-realcompact if and only if each c-stable family of closed sets in X with finite intersection property has nonempty intersection. This last condition which makes sense for an arbitrary topological space can be taken as an alternative definition of a c-realcompact space. We show that each topological space can be extended as a dense subspace to a c-realcompact space with some desired extension properties. An allied class of spaces viz CP-compact spaces akin to that of c-realcompact spaces are introduced. The paper ends after examining how far a known class of c-realcompact spaces could be realized as CP-compact for appropriately chosen ideal P of closed sets in X.</pre>

Alexander's theorem for real-compactness

1968 ◽  
Vol 64 (1) ◽  
pp. 41-43 ◽  
Author(s):  
Allan Hayes
Keyword(s):  
Topological Space ◽  
Intersection Property ◽  
Finite Intersection ◽  
Closed Sets ◽  
Empty Intersection ◽  
Finite Intersection Property

Alexander's theorem (5) states that a topological space is compact if there is a sub-base, , for its closed sets such that every subclass of with the finite intersection property has a non-empty intersection. An analysis and extension of this is given here which has applications, inter alia, to problems concerning real-compactness (2).

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 Infra Soft Compact Spaces and Application to Fixed Point Theorem

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Tareq M. Al-shami
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Topological Properties ◽  
Finite Product ◽  
Finite Intersection ◽  
Compact Spaces ◽  
Closed Sets ◽  
Soft Topology ◽  
Covering Properties

Infra soft topology is one of the recent generalizations of soft topology which is closed under finite intersection. Herein, we contribute to this structure by presenting two kinds of soft covering properties, namely, infra soft compact and infra soft Lindelöf spaces. We describe them using a family of infra soft closed sets and display their main properties. With the assistance of examples, we mention some classical topological properties that are invalid in the frame of infra soft topology and determine under which condition they are valid. We focus on studying the “transmission” of these concepts between infra soft topology and classical infra topology which helps us to discover the behaviours of these concepts in infra soft topology using their counterparts in classical infra topology and vice versa. Among the obtained results, these concepts are closed under infra soft homeomorphisms and finite product of soft spaces. Finally, we introduce the concept of fixed soft points and reveal main characterizations, especially those induced from infra soft compact spaces.

Characterization of Fuzzy δg*-Closed Sets in Fuzzy Topological Spaces

2016 ◽  
Vol 5 (2) ◽  
pp. 1-12
Author(s):  
Anahid Kamali ◽  
Hamid Reza Moradi
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Topological Spaces ◽  
Basic Properties ◽  
Closed Sets ◽  
Research Article ◽  
Classical Paper ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The purpose of this research article is to explain the meaning of g-closed sets in fuzzy topological spaces, which is more understandable to the readers and we find some of its basic properties. The concept of fuzzy sets was introduced by Zadeh in his classical paper (1965). Thereafter many investigations have been carried out, in the general theoretical field and also in different applied areas, based on this concept. The idea of fuzzy topological space was introduced by Chang (1968). The idea is more or less a generalization of ordinary topological spaces. Different aspects of such spaces have been developed, by several investigators. This paper is also devoted to the development of the theory of fuzzy topological spaces.

A quasi-uniform characterization of Wallman type compactifications

2003 ◽  
Vol 40 (1-2) ◽  
pp. 257-267 ◽  
Author(s):  
S. Romaguera ◽  
M. A. Sánchez-Granero
Keyword(s):  
Topological Space ◽  
Uniform Space ◽  
Dense Subspace ◽  
Totally Bounded ◽  
Hausdorff Compactifications

A *-compactification of a T1 quasi-uniform space (X,U) is a compact T1 quasi-uniform space (Y,V) that has a T(V*)-dense subspace quasi-isomorphic to (X,U), where V* denotes the coarsest uniformity finer than V.In this paper we characterize all Wallman type compactifications of a T1 topological space in terms of the *-compactification of its point symmetric totally bounded transitive compatible quasi-uniformities. We deduce that the *-compactification of the Pervin quasi-uniformity of any normal T1 topological space X is exactly the Stone-Cech compactification of X. We also obtain a characterization of those Hausdorff compactifications of a given space, which are of Wallman type.

Weak Normality and Related Properties

1970 ◽  
Vol 22 (5) ◽  
pp. 997-1001
Author(s):  
Eugene S. Ball
Keyword(s):  
Positive Integer ◽  
Topological Space ◽  
Closed Set ◽  
Common Part ◽  
Closed Sets ◽  
Open Set ◽  
Point Set ◽  
Weak Normality ◽  
Definition Of

In [5], Zenor stated the definition of weakly normal. In the main, since weak normality does not imply either normality or regularity, various properties related to either normality or regularity will be considered in the context of weak normality.Throughout this paper the word “space” will mean topological space. The closure of a point set M will be denoted by cl(M). The closure of a point set M with respect to the subspace K will be denoted by cl(M, K).Definition 1. A space S is weakly normal provided that if is a monotonically decreasing sequence of closed sets in S with no common part and H is a closed set in S not intersecting H1, then there is a positive integer N and an open set D such that HN ⊂ D and cl(D) does not intersect H.

scholarly journals Characterization of Soft S-Open Sets in Bi-Soft Topological Structure Concerning Crisp Points

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2100
Author(s):  
Arif Mehmood ◽  
Mohammed M. Al-Shomrani ◽  
Muhammad Asad Zaighum ◽  
Saleem Abdullah
Keyword(s):  
Coordinate Space ◽  
Regular Space ◽  
Topological Spaces ◽  
Finite Intersection ◽  
Open Set ◽  
Separation Axioms ◽  
Finite Intersection Property ◽  
Almost All ◽  
Bitopological Spaces

In this article, a soft s-open set in soft bitopological structures is introduced. With the help of this newly defined soft s-open set, soft separation axioms are regenerated in soft bitopological structures with respect to crisp points. Soft continuity at some certain points, soft bases, soft subbase, soft homeomorphism, soft first-countable and soft second-countable, soft connected, soft disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. The product of two soft  axioms with respect crisp points with almost all possibilities in soft bitopological spaces relative to semiopen sets are introduced. In addition to this, soft (countability, base, subbase, finite intersection property, continuity) are addressed with respect to semiopen sets in soft bitopological spaces. Product of soft first and second coordinate spaces are addressed with respect to semiopen sets in soft bitopological spaces. The characterization of soft separation axioms with soft connectedness is addressed with respect to semiopen sets in soft bitopological spaces. In addition to this, the product of two soft topological spaces is (  space if each coordinate space is soft  space, product of two sot topological spaces is (S regular and C regular) space if each coordinate space is (S regular and C regular), the product of two soft topological spaces is connected if each coordinate space is soft connected and the product of two soft topological spaces is (first-countable, second-countable) if each coordinate space is (first countable, second-countable).

scholarly journals F-Rings of Continuous Functions I

1959 ◽  
Vol 11 ◽  
pp. 80-86 ◽  
Author(s):  
Barron Brainerd
Keyword(s):  
Topological Space ◽  
Banach Algebra ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
The Other ◽  
Topological Spaces ◽  
Closed Sets ◽  
Real Complex

It is well known (2, 4) that the ring of all real (complex) continuous functions on a compact Hausdorff space can be characterized algebraically as a Banach algebra which satisfies certain additional intrinsic conditions. It might be expected that rings of all continuous functions on other topological spaces also have algebraic characterizations. The main purpose of this note is to discuss two such characterizations. In both cases the characterizations are given in the terms of the theory of F-brings (1). In one case a characterization is given for the ring of all (real) continuous functions on a generalized P-space, that is, a zero-dimensional topological space in which the class of open-closed sets forms a σ-algebra. A Hausdorff generalized P-space is a P-space in the terminology of (3). In the other case a theorem of Sikorski (6) is employed to give a characterization of the ring of all (real) continuous functions on an upper X1-compact P-space.

Definitions of compact

1990 ◽  
Vol 55 (2) ◽  
pp. 645-655 ◽  
Author(s):  
Paul E. Howard
Keyword(s):  
Accumulation Point ◽  
Infinite Subset ◽  
Nonempty Intersection ◽  
Topological Spaces ◽  
Finite Intersection ◽  
Original Proof ◽  
Closed Sets ◽  
Finite Intersection Property ◽  
The Axiom Of Choice ◽  
Tychonoff Theorem

Several definitions of “compact” for topological spaces have appeared in the literature (see [5]). We will consider the following:Definition. A topological space X is1. Compact(1) if every open cover of X has a finite subcover.2. Compact(2) if every infinite subset E of X has a complete accumulation point (i.e., a point x0 ∈ X such that for every neighborhood U of x0, |E ∩ U| = |E|).3. Compact(3) if there is a subbase S for the topology on X such that every cover of X by members of S has a finite subcover.4. Compact(4) if each nest of closed, nonempty sets has a nonempty intersection.5. Compact(5) if every family of closed sets in X which has the finite intersection property (every finite subfamily has a nonempty intersection) has a nonempty intersection.6. Compact(6) if each net in X has a cluster point.7. Compact(7) if each net in X has a convergent subnet.This work was motivated primarily by consideration of various proofs that the Tychonoff theorem, T (“the product of compact topological spaces is compact”) is equivalent to the Axiom of Choice, AC. Tychonoff's original proof that AC implies T used Definition 2 [13]. Other proofs have used Definitions 3 and 5; see [5]. The proof by Kelley that T implies AC uses Definition 5 [6].

scholarly journals Experimental Evaluation of Shear Behavior of Stone Masonry Wall

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2313
Author(s):  
Maria Luisa Beconcini ◽  
Pietro Croce ◽  
Paolo Formichi ◽  
Filippo Landi ◽  
Benedetta Puccini
Keyword(s):  
Shear Behavior ◽  
Stone Masonry ◽  
Masonry Walls ◽  
Mechanical Parameters ◽  
In Situ Tests ◽  
Capacity Curves ◽  
Historical Structures ◽  
Definition Of

The evaluation of the shear behavior of masonry walls is a first fundamental step for the assessment of existing masonry structures in seismic zones. However, due to the complexity of modelling experimental behavior and the wide variety of masonry types characterizing historical structures, the definition of masonry’s mechanical behavior is still a critical issue. Since the possibility to perform in situ tests is very limited and often conflicting with the needs of preservation, the characterization of shear masonry behavior is generally based on reference values of mechanical properties provided in modern structural codes for recurrent masonry categories. In the paper, a combined test procedure for the experimental characterization of masonry mechanical parameters and the assessment of the shear behavior of masonry walls is presented together with the experimental results obtained on three stone masonry walls. The procedure consists of a combination of three different in situ tests to be performed on the investigated wall. First, a single flat jack test is executed to derive the normal compressive stress acting on the wall. Then a double flat jack test is carried out to estimate the elastic modulus. Finally, the proposed shear test is performed to derive the capacity curve and to estimate the shear modulus and the shear strength. The first results obtained in the experimental campaign carried out by the authors confirm the capability of the proposed methodology to assess the masonry mechanical parameters, reducing the uncertainty affecting the definition of capacity curves of walls and consequently the evaluation of seismic vulnerability of the investigated buildings.

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