separation axiom
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2021 ◽  
Vol 34 (4) ◽  
pp. 45-57
Author(s):  
Hammood A. A ◽  
Esmaeel R. B

    In this paper, the concept of soft closed groups is presented using the soft ideal pre-generalized open and soft pre-open, which are -á¶…- - -closed sets " -closed", Which illustrating several characteristics of these groups.  We also use some games and   -  Separation Axiom, such as (Æ®0, Ó¼, á¶…) that use many tables and charts to illustrate this. Also, we put some proposals to study the relationship between these games and give some examples.


2021 ◽  
Vol 3 (1) ◽  
pp. 9-15
Author(s):  
B. Alkasasbeh ◽  
H. Hdeib

In this paper we discuss some pairwise properly hereditary properties concerning pairwise separation axiom, and obtain several results related to these properties.


2020 ◽  
Vol 63 (1) ◽  
pp. 197-203 ◽  
Author(s):  
Angelo Bella ◽  
Santi Spadaro

AbstractWe present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s solution to Alexandroff’s problem: A survey, Topology Appl. 153(2006), 2199–2217).In contrast to previous attempts, we do not need any separation axiom beyond $T_{2}$.


2019 ◽  
Vol 6 (2) ◽  
pp. 13-19
Author(s):  
Basim M. Melgat ◽  
Munir Abdul Khalik AL-Khafaji

"In this paper, we study fuzzy separation axiom in the fuzzy topological ring space. Also the relationship between the types of fuzzy separation axiom was studied.


Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1072 ◽  
Author(s):  
Sang-Eon Han ◽  
Saeid Jafari ◽  
Jeong Kang

The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies on Z n which are not homeomorphic to the typical n-dimensional Khalimsky topological space. Based on these different types of new topological structures on Z n , many new mathematical approaches can be done in the fields of pure and applied sciences, such as fixed point theory, rough set theory, and so on.


2019 ◽  
Vol S (01) ◽  
pp. 706-709
Author(s):  
Maragatha Meenakshi P. ◽  
Chandran S.

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 1889-1901 ◽  
Author(s):  
Sang-Eon Han

The present paper studies certain low-level separation axioms of a topological space, denoted by A(X), induced by a geometric AC-complex X. After proving that whereas A(X) is an Alexandroff space satisfying the semi-T1 2 -separation axiom, we observe that it does neither satisfy the pre T1 2 -separation axiom nor is a Hausdorff space. These are main motivations of the present work. Although not every A(X) is a semi-T1 space, after proceeding with an edge to edge tiling (or a face to face crystallization) of Rn, n ? N, denoted by T(Rn) as an AC complex, we prove that A(T(Rn)) is a semi-T1 space. Furthermore, we prove that A(En), induced by an nD Cartesian AC complex Cn = (En,N,dim), is also a semi-T1 space, n ? N. The paper deals with AC-complexes with the locally finite (LF-, for brevity) property, which can be used in the fields of pure and applied mathematics as well as digital topology, computational topology, and digital geometry.


2018 ◽  
Vol 7 (4.10) ◽  
pp. 766
Author(s):  
Govardhana Reddy H G ◽  
Basavaraj M. Ittanagi

Study and investigate a class of separation axiom namely gg-Tk space (k=0, 1, 2), gg-regular and gg-normal space. Meanwhile, some of their properties are obtained. 


Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4689-4700 ◽  
Author(s):  
Sang-Eon Han

The paper studies the open-hereditary property of semi-separation axioms and applies it to the study of digital topological spaces such as an n-dimensional Khalimsky topological space, a Marcus-Wyse topological space and so on. More precisely, we study various properties of digital topological spaces related to low-level and semi-separation axioms such as T1/2 , semi-T1/2 , semi-T1, semi-T2, etc. Besides, using the finite or the infinite product property of the semi-Ti-separation axiom, i ? {1,2}, we prove that the n-dimensional Khalimsky topological space is a semi-T2-space. After showing that not every subspace of the digital topological spaces satisfies the semi-Ti-separation axiom, i ?{1,2}, we prove that the semi-Tiseparation property is open-hereditary, i ? {1,2}. All spaces in the paper are assumed to be nonempty and connected.


2017 ◽  
Vol 11 (01) ◽  
pp. 1850010
Author(s):  
Josephine Josol Baculta ◽  
Helen Moso Rara

The purpose of this paper is to introduce and investigate some [Formula: see text] separation axioms in bigeneralized topological spaces. Using the concepts of regular generalized star b-open sets due to Indirani and Sindhu, the study defines and characterizes [Formula: see text]-[Formula: see text], [Formula: see text]-[Formula: see text], [Formula: see text]-regular and [Formula: see text]-normal spaces.


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