scholarly journals Sum of the spaces on ordered setting

2020 ◽  
Vol 6 (2) ◽  
pp. 255-265
Author(s):  
T. M. Al-shami
Keyword(s):  
Pairwise Disjoint ◽  
Compact Spaces ◽  
Separation Axioms ◽  
Continuous Maps ◽  
Ordered Space

AbstractOne of the divergences between topology and ordered topology is that some topological concepts such as separation axioms and continuous maps are defined using open neighborhoods or neighborhoods without any difference, however, they are distinct on the ordered topology according to the neighborhoods: Are they open neighborhoods or not? In this paper, we present the concept of sum of the ordered spaces using pairwise disjoint topological ordered spaces and study main properties. Then, we introduce the properties of ordered additive, finitely ordered additive and countably ordered additive which associate topological ordered spaces with their sum. We prove that the properties of being Ti-ordered and strong Ti-ordered spaces are ordered additive, however, the properties of monotonically compact and ordered compact spaces are finitely ordered additive. Also, we define a mapping between two sums of the ordered spaces using mappings between the ordered spaces and deduce some results related to some types of continuity and homeomorphism. We complete this work by determining the conditions under which a topological ordered space is sum of the ordered spaces.

scholarly journals Soft Simply Compact Spaces

2020 ◽  
pp. 108-113
Author(s):  
S. Noori ◽  
Y. Y. Yousif
Keyword(s):  
Topological Spaces ◽  
Compact Spaces ◽  
Open Set ◽  
Separation Axioms

The aim of this research is to use the class of soft simply open set to define new types of separation axioms in soft topological spaces. We also introduce and study the concept of soft simply compactness.

scholarly journals Separation axioms of αm-contra-open maps and b-ω-open sets in generalized topological spaces

2021 ◽  
Vol 40 (5) ◽  
pp. 1249-1266
Author(s):  
Boulbaba Ghanmi ◽  
Rim Messaoud ◽  
Amira Missaoui
Keyword(s):  
Topological Spaces ◽  
Separation Axioms ◽  
Continuous Maps ◽  
Open Maps

In this paper, we introduce Tαm-Super-Spaces, αm-contra-closed maps, αm-contra-open maps, αm-contra-continuous maps, αm-contrairresolute maps, b-ω-open sets and Continuity via b-ω-open sets and studied some of their properties

scholarly journals A functor IS in the Category Compact Hausdorff Spaces

2020 ◽  
Vol 6 (3) ◽  
pp. 13-22
Author(s):  
Kh. Kurbanov ◽  
S. Yodgarov
Keyword(s):  
Hausdorff Spaces ◽  
Normal Functor ◽  
Compact Spaces ◽  
Continuous Maps

We construct a space of normed, homogeneous and max-plus-semiadditive functionals and we give its description. Further we establish that the construction of taking of a space of normed, homogeneous and max-plus-semiadditive functionals, forms a normal functor acting in the category of Hausdorff compact spaces and their continuous maps.

scholarly journals CHAINS OF FUNCTIONS IN -SPACES

2015 ◽  
Vol 99 (3) ◽  
pp. 350-363 ◽  
Author(s):  
TOMASZ KANIA ◽  
RICHARD J. SMITH
Keyword(s):  
Linear Operators ◽  
Partial Ordering ◽  
Hausdorff Spaces ◽  
Weakly Compact ◽  
Compact Spaces ◽  
Classical Work ◽  
Ordered Space ◽  
Weakly Compact Operators ◽  
Topology Of Pointwise Convergence ◽  
Corson Compact

The Bishop property (♗), introduced recently by K. P. Hart, T. Kochanek and the first-named author, was motivated by Pełczyński’s classical work on weakly compact operators on $C(K)$-spaces. This property asserts that certain chains of functions in said spaces, with respect to a particular partial ordering, must be countable. There are two versions of (♗): one applies to linear operators on $C(K)$-spaces and the other to the compact Hausdorff spaces themselves. We answer two questions that arose after (♗) was first introduced. We show that if $\mathscr{D}$ is a class of compact spaces that is preserved when taking closed subspaces and Hausdorff quotients, and which contains no nonmetrizable linearly ordered space, then every member of $\mathscr{D}$ has (♗). Examples of such classes include all $K$ for which $C(K)$ is Lindelöf in the topology of pointwise convergence (for instance, all Corson compact spaces) and the class of Gruenhage compact spaces. We also show that the set of operators on a $C(K)$-space satisfying (♗) does not form a right ideal in $\mathscr{B}(C(K))$. Some results regarding local connectedness are also presented.

On Homogeneous Images of Compact Ordered Spaces

1993 ◽  
Vol 45 (2) ◽  
pp. 380-393 ◽  
Author(s):  
J. Nikiel ◽  
E.D. Tymchatyn
Keyword(s):  
Pairwise Disjoint ◽  
Continuous Image ◽  
Closed Curves ◽  
Ordered Space ◽  
Continuous Images

AbstractWe answer a 1975 question of G R Gordh by showing that if X is a homogeneous compactum which is the continuous image of a compact ordered space then at least one of the following holds(I) X is metrizable, (II) dim X = 0 or (III) X is a union of finitely many pairwise disjoint generalized simple closed curves.We begin to examine the structure of homogeneous 0-dimensional spaces which are continuous images of ordered compacta.

scholarly journals Compactness on Soft Topological Ordered Spaces and Its Application on the Information System

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
T. M. Al-shami
Keyword(s):  
Information System ◽  
Missing Values ◽  
Product Spaces ◽  
Finite Product ◽  
Soft Sets ◽  
Finite Intersection ◽  
Compact Spaces ◽  
Ordered Space ◽  
Finite Spaces ◽  
Soft Topological Space

It is well known every soft topological space induced from soft information system is soft compact. In this study, we integrate between soft compactness and partially ordered set to introduce new types of soft compactness on the finite spaces and investigate their application on the information system. First, we initiate a notion of monotonic soft sets and establish its main properties. Second, we introduce the concepts of monotonic soft compact and ordered soft compact spaces and show the relationships between them with the help of examples. We give a complete description for each one of them by making use of the finite intersection property. Also, we study some properties associated with some soft ordered spaces and finite product spaces. Furthermore, we investigate the conditions under which these concepts are preserved between the soft topological ordered space and its parametric topological ordered spaces. In the end, we provide an algorithm for expecting the missing values of objects on the information system depending on the concept of ordered soft compact spaces.

Cliquishness and Quasicontinuity of Two-Variable Maps

2013 ◽  
Vol 56 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. Bouziad
Keyword(s):  
Wide Class ◽  
Metric Space ◽  
Winning Strategy ◽  
Positive Answer ◽  
Baire Space ◽  
Compact Spaces ◽  
Open Set ◽  
Continuous Maps ◽  
Dense Set

AbstractWe study the existence of continuity points for mappingswhose x-sectionsare fragmentable and y-sectionsare quasicontinuous, where X is a Baire space and Z is a metric space. For the factor Y, we consider two infinite “pointpicking” games G1(y) and G2(y) defined respectively for each y ∈ Y as follows: in the n-th inning, Player I gives a dense set Dn⊂ Y, respectively, a dense open set Dn⊂ Y. Then Player II picks a point yn∈ Dn; II wins if y is in the closure of {yn: n ∈ N}, otherwise I wins. It is shown that (i) f is cliquish if II has a winning strategy in G1(y) for every y ∈ Y, and (ii) f is quasicontinuous if the x-sections of f are continuous and the set of y ∈ Y such that II has a winning strategy in G2(y) is dense in Y. Item (i) extends substantially a result of Debs and item (ii) indicates that the problem of Talagrand on separately continuous maps has a positive answer for a wide class of “small” compact spaces.

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