scholarly journals S-paracompactness and S2-paracompactness

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5645-5650
Author(s):  
Ohud Alghamdi ◽  
Lutfi Kalantan ◽  
Wafa Alagal
Keyword(s):  
Topological Space ◽  
Restriction Map ◽  
Paracompact Space ◽  
Separable Subspace ◽  
Bijective Function

A topological space X is an S-paracompact if there exists a bijective function f from X onto a paracompact space Y such that for every separable subspace A of X the restriction map f|A from A onto f (A) is a homeomorphism. Moreover, if Y is Hausdorff, then X is called S2-paracompact. We investigate these two properties.

scholarly journals Results on C2-paracompactness

2021 ◽  
Vol 14 (2) ◽  
pp. 351-357
Author(s):  
Hala Alzumi ◽  
Lutfi Kalantan ◽  
Maha Mohammed Saeed
Keyword(s):  
Topological Space ◽  
Paracompact Space ◽  
Compact Subspace ◽  
Bijective Function

A C-paracompact is a topological space X associated with a paracompact space Y and a bijective function f : X −→ Y satisfying that f A: A −→ f(A) is a homeomorphism for each compact subspace A ⊆ X. Furthermore, X is called C2-paracompact if Y is T2 paracompact. In this article, we discuss the above concepts and answer the problem of Arhangel’ski ̆i. Moreover, we prove that the sigma product Σ(0) can not be condensed onto a T2 paracompact space.

scholarly journals EXTENSION OF CONTINUOUS MAPPINGS AND H1-RETRACTS

2008 ◽  
Vol 78 (3) ◽  
pp. 497-506 ◽  
Author(s):  
OLENA KARLOVA
Keyword(s):  
Topological Space ◽  
Continuous Mapping ◽  
Paracompact Space ◽  
Open Set ◽  
Continuous Mappings ◽  
Arbitrary Topological Space ◽  
Completely Metrizable

AbstractWe prove that any continuous mapping f:E→Y on a completely metrizable subspace E of a perfect paracompact space X can be extended to a Lebesgue class one mapping g:X→Y (that is, for every open set V in Y the preimage g−1(V ) is an Fσ-set in X) with values in an arbitrary topological space Y.

scholarly journals P-Normality

2021 ◽  
Vol 12 (6) ◽  
pp. 1-8
Author(s):  
LUTFI KALANTAN ◽  
MAI MANSOURI
Keyword(s):  
Topological Space ◽  
Normal Space ◽  
Bijective Function

A topological space X is called P-normal if there exist a normal space Y and a bijective function f : X −→ Y such that the restriction f|A : A −→ f(A) is a homeomorphism for each paracompact subspace A ⊆ X. We will investigate this property and produce some examples to illustrate the relation between P-normality and other weaker kinds of normality.

scholarly journals Study about fuzzyω-paracompact space in fuzzy topological space

2020 ◽  
Vol 1591 ◽  
pp. 012067
Author(s):  
Munir Abdul Khalik AL-Khafaji ◽  
Gazwan Haider Abdulhusein
Keyword(s):  
Topological Space ◽  
Paracompact Space ◽  
Fuzzy Topological Space

scholarly journals C-normal topological property

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 407-411 ◽  
Author(s):  
Samirah AlZahrani ◽  
Lutfi Kalantan
Keyword(s):  
Topological Space ◽  
Topological Property ◽  
Normal Space ◽  
Compact Subspace ◽  
Bijective Function

A topological space X is called C-normal if there exist a normal space Y and a bijective function f : X ? Y such that the restriction f _ C : C ? f (C) is a homeomorphism for each compact subspace C ? X. We investigate this property and present some examples to illustrate the relationships between C-normality and other weaker kinds of normality.

COMBINATORIAL POLYNOMIALLY COMPUTABLE CHARACTERISTICS OF SUBSTITUTIONS AND THEIR PROPERTIES

2020 ◽  
Vol 7 (2) ◽  
pp. 34-41
Author(s):  
VLADIMIR NIKONOV ◽  
◽  
ANTON ZOBOV ◽  
Keyword(s):  
Mathematical Expectation ◽  
Point Of View ◽  
Small Range ◽  
Computational Point ◽  
Wide Range ◽  
Bijective Function ◽  
The Difference ◽  
Element Base ◽  
Selection Of

The construction and selection of a suitable bijective function, that is, substitution, is now becoming an important applied task, particularly for building block encryption systems. Many articles have suggested using different approaches to determining the quality of substitution, but most of them are highly computationally complex. The solution of this problem will significantly expand the range of methods for constructing and analyzing scheme in information protection systems. The purpose of research is to find easily measurable characteristics of substitutions, allowing to evaluate their quality, and also measures of the proximity of a particular substitutions to a random one, or its distance from it. For this purpose, several characteristics were proposed in this work: difference and polynomial, and their mathematical expectation was found, as well as variance for the difference characteristic. This allows us to make a conclusion about its quality by comparing the result of calculating the characteristic for a particular substitution with the calculated mathematical expectation. From a computational point of view, the thesises of the article are of exceptional interest due to the simplicity of the algorithm for quantifying the quality of bijective function substitutions. By its nature, the operation of calculating the difference characteristic carries out a simple summation of integer terms in a fixed and small range. Such an operation, both in the modern and in the prospective element base, is embedded in the logic of a wide range of functional elements, especially when implementing computational actions in the optical range, or on other carriers related to the field of nanotechnology.

The Spatial Dimensions of Social Networks

2020 ◽  
pp. 367-383
Author(s):  
Zachary P. Neal
Keyword(s):  
Social Networks ◽  
Topological Space ◽  
Network Science ◽  
Spatial Dimensions

The first law of geography holds that everything is related to everything else, but near things are more related than distant things, where distance refers to topographical space. If a first law of network science exists, it would similarly hold that everything is related to everything else, but near things are more related than distant things, but where distance refers to topological space. Frequently these two laws collide, together holding that everything is related to everything else, but topographically and topologically near things are more related than topographically and topologically distant things. The focus of the spatial study of social networks lies in exploring a series of questions embedded in this combined law of geography and networks. This chapter explores the questions that have been asked and the answers that have been offered at the intersection of geography and networks.

On a topological construction of Juhasz and Shelah

1992 ◽  
Vol 57 (1) ◽  
pp. 166-171
Author(s):  
Dan Velleman
Keyword(s):  
Topological Space ◽  
Additional Structure ◽  
Homogeneous Set ◽  
Stationary Set ◽  
Topological Construction

In [2], Juhasz and Shelah use a forcing argument to show that it is consistent with GCH that there is a 0-dimensional T2 topological space X of cardinality ℵ3 such that every partition of the triples of X into countably many pieces has a nondiscrete (in the topology) homogeneous set. In this paper we will show how to construct such a space using a simplified (ω2, 1)-morass with certain additional structure added to it. The additional structure will be a slight strengthening of a built-in ◊ sequence, analogous to the strengthening of ordinary ◊k to ◊S for a stationary set S ⊆ k.Suppose 〈〈θα∣ ∝ ≤ ω2〉, 〈∝β∣α < β ≤ ω2〉〉 is a neat simplified (ω2, 1)-morass (see [3]). Let ℒ be a language with countably many symbols of all types, and suppose that for each α < ω2, α is an ℒ-structure with universe θα. The sequence 〈α∣α < ω2 is called a built-in ◊ sequence for the morass if for every ℒ-structure with universe ω3 there is some α < ω2 and some f ∈αω2 such that f(α) ≺ , where f(α) is the ℒ-structure isomorphic to α under the isomorphism f. We can strengthen this slightly by assuming that α is only defined for α ∈ S, for some stationary set S ⊆ ω2. We will then say that is a built-in ◊ sequence on levels in S if for every ℒ-structure with universe ω3 there is some α ∈ S and some f ∈ αω2 such that f(α) ≺ .

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