scholarly journals Some Results in Neutrosophic Soft Topology Concerning Neutrosophic Soft ∗ b Open Sets

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Arif Mehmood ◽  
Saleem Abdullah ◽  
Mohammed M. Al-Shomrani ◽  
Muhammad Imran Khan ◽  
Orawit Thinnukool
Keyword(s):  
Compact Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Soft Topology ◽  
Open Set ◽  
Topological Features ◽  
Separation Axioms ◽  
Countable Space ◽  
Countably Compact

In this article, new generalised neutrosophic soft open known as neutrosophic soft ∗ b open set is introduced in neutrosophic soft topological spaces. Neutrosophic soft ∗ b open set is generated with the help of neutrosophic soft semiopen and neutrosophic soft preopen sets. Then, with the application of this new definition, some soft neutrosophical separation axioms, countability theorems, and countable space can be Hausdorff space under the subjection of neutrosophic soft sequence which is convergent, the cardinality of neutrosophic soft countable space, engagement of neutrosophic soft countable and uncountable spaces, neutrosophic soft topological features of the various spaces, soft neutrosophical continuity, the product of different soft neutrosophical spaces, and neutrosophic soft countably compact that has the characteristics of Bolzano Weierstrass Property (BVP) are studied. In addition to this, BVP shifting from one space to another through neutrosophic soft continuous functions, neutrosophic soft sequence convergence, and its marriage with neutrosophic soft compact space, sequentially compactness are addressed.

scholarly journals Intuitionistic Fuzzy Topological Spaces Model

2020 ◽  
Vol 55 (2) ◽  
Author(s):  
Hind Fadhil Abbas
Keyword(s):  
Hausdorff Space ◽  
Basic Structure ◽  
Normal Space ◽  
Regular Space ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Separation Axioms ◽  
Fuzzy Ideal ◽  
Scientific Phenomenon ◽  
Fuzzy Topological Spaces

The fusion of technology and science is a very complex and scientific phenomenon that still carries mysteries that need to be understood. To unravel these phenomena, mathematical models are beneficial to treat different systems with unpredictable system elements. Here, the generalized intuitionistic fuzzy ideal is studied with topological space. These concepts are useful to analyze new generalized intuitionistic models. The basic structure is studied here with various relations between the generalized intuitionistic fuzzy ideals and the generalized intuitionistic fuzzy topologies. This study includes intuitionistic fuzzy topological spaces (IFS); the fundamental definitions of intuitionistic fuzzy Hausdorff space; intuitionistic fuzzy regular space; intuitionistic fuzzy normal space; intuitionistic fuzzy continuity; operations on IFS, the compactness and separation axioms.

scholarly journals On Certain Covering Properties and Minimal Sets of Bigeneralized Topological Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1145
Author(s):  
Samer Al Ghour ◽  
Abdullah Alhorani
Keyword(s):  
Topological Spaces ◽  
Minimal Sets ◽  
Open Set ◽  
Covering Properties ◽  
Countably Compact

We introduce q-Lindelöf, u-Lindelöf, p-Lindelöf, s-Lindelöf, q-countably-compact, u-countably-compact, p-countably-compact, and s-countably-compact as new covering concepts in bigeneralized topological spaces via q-open sets and u-open sets in bigeneralized topological spaces. Relationships between them are studied. As two symmetries relationships, we show that q-Lindelöf and u-Lindelöf are equivalent concepts, and that q-countably-compact and u-countably-compact are equivalent concepts. We focus on continuity images of these covering properties. Finally, we define and investigate minimal q-open set, minimal u-open set, and minimal s-open sets as three new types of minimality in bigeneralized topological spaces.

TWO SPACES OF MINIMAL PRIMES

2012 ◽  
Vol 11 (01) ◽  
pp. 1250014 ◽  
Author(s):  
PAPIYA BHATTACHARJEE
Keyword(s):  
Compact Space ◽  
Hausdorff Space ◽  
Topological Spaces ◽  
Zariski Topology ◽  
Topological Properties ◽  
Locally Compact ◽  
Inverse Topology ◽  
Minimal Prime ◽  
Stone Spaces ◽  
Prime Elements

This paper studies algebraic frames L and the set Min (L) of minimal prime elements of L. We will endow the set Min (L) with two well-known topologies, known as the Hull-kernel (or Zariski) topology and the inverse topology, and discuss several properties of these two spaces. It will be shown that Min (L) endowed with the Hull-kernel topology is a zero-dimensional, Hausdorff space; whereas, Min (L) endowed with the inverse topology is a T1, compact space. The main goal will be to find conditions on L for the spaces Min (L) and Min (L)-1 to have various topological properties; for example, compact, locally compact, Hausdorff, zero-dimensional, and extremally disconnected. We will also discuss when the two topological spaces are Boolean and Stone 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 On β-Open Sets and Ideals in Topological Spaces

2019 ◽  
Vol 12 (3) ◽  
pp. 893-905
Author(s):  
Glaisa T. Catalan ◽  
Roberto N. Padua ◽  
Michael Jr. Patula Baldado
Keyword(s):  
Topological Space ◽  
Compact Space ◽  
Topological Spaces ◽  
Open Set ◽  
Separated Sets ◽  
The Ideal

Let X be a topological space and I be an ideal in X. A subset A of a topological space X is called a β-open set if A ⊆ cl(int(cl(A))). A subset A of X is called β-open with respect to the ideal I, or βI -open, if there exists an open set U such that (1) U − A ∈ I, and (2) A − cl(int(cl(U))) ∈ I. A space X is said to be a βI -compact space if it is βI -compact as a subset. An ideal topological space (X, τ, I) is said to be a cβI -compact space if it is cβI -compact as a subset. An ideal topological space (X, τ, I) is said to be a countably βI -compact space if X is countably βI -compact as a subset. Two sets A and B in an ideal topological space (X, τ, I) is said to be βI -separated if clβI (A) ∩ B = ∅ = A ∩ clβ(B). A subset A of an ideal topological space (X, τ, I) is said to be βI -connected if it cannot be expressed as a union of two βI -separated sets. An ideal topological space (X, τ, I) is said to be βI -connected if X βI -connected as a subset. In this study, we introduced the notions βI -open set, βI -compact, cβI -compact, βI -hyperconnected, cβI -hyperconnected, βI -connected and βI -separated. Moreover, we investigated the concept β-open set by determining some of its properties relative to the above-mentioned notions.

scholarly journals Some applications of minimal open sets

2001 ◽  
Vol 27 (8) ◽  
pp. 471-476 ◽  
Author(s):  
Fumie Nakaoka ◽  
Nobuyuki Oda
Keyword(s):  
Hausdorff Space ◽  
Nonempty Subset ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Locally Finite ◽  
Open Set ◽  
Finite Space

We characterize minimal open sets in topological spaces. We show that any nonempty subset of a minimal open set is pre-open. As an application of a theory of minimal open sets, we obtain a sufficient condition for a locally finite space to be a pre-Hausdorff space.

scholarly journals Averaging operators on the ring of continuous functions on a compact space

1964 ◽  
Vol 4 (3) ◽  
pp. 293-298 ◽  
Author(s):  
Barron Brainerd
Keyword(s):  
Compact Space ◽  
Linear Transformation ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Topological Product ◽  
Averaging Operators ◽  
Averaging Operator ◽  
Ring Of Continuous Functions ◽  
Image Position

In this note we answer the following question: Given C(X) the latticeordered ring of real continuous functions on the compact Hausdorff space X and T an averaging operator on C(X), under what circumstances can X be decomposed into a topological product such that supports a measure m and Tf = h where By an averaging operator we mean a linear transformation T on C(X) such that: 1. T is positive, that is, if f>0 (f(x) ≧ 0 for all x ∈ and f(x) > 0 for some a ∈ X), then Tf>0. 2. T(fTg) = (Tf)(Tg). 3. T l = 1 where l(x) = 1 for all x ∈ X.

scholarly journals Separation Axioms Interval-Valued Fuzzy Soft Topology via Quasi-Neighbourhood Structure

2019 ◽  
Author(s):  
Mabruka Ali ◽  
Adem Kılıçman ◽  
Azadeh Zahedi Khameneh
Keyword(s):  
Topological Spaces ◽  
Basic Properties ◽  
Soft Topology ◽  
Separation Axioms ◽  
Neighbourhood Structure ◽  
Soft Point ◽  
Interval Valued

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

scholarly journals Certain Features of Fuzzy Contra-continuous functions

1970 ◽  
Vol 32 (1) ◽  
pp. 71-77
Author(s):  
MH Rashid ◽  
DM Ali
Keyword(s):  
Compact Space ◽  
Continuous Functions ◽  
Subject Classification ◽  
Topological Spaces ◽  
Fuzzy Graph ◽  
Closed Space ◽  
Ams Subject Classification ◽  
Fuzzy Topological Spaces ◽  
Academy Of Sciences

We deal with fuzzy topological spaces, fuzzy compact space, fuzzy S-closed space, fuzzy graph, fuzzy continuous functions and fuzzy LC-continuous functions. In this paper, we introduce the concepts of fuzzy contra-continuities and explore properties and relationships of such types of functions. Keywords: fuzzy contra-continuity, fuzzy S-closed space, fuzzy graph. AMS Subject Classification: 54A40. doi: 10.3329/jbas.v32i1.2444 Journal of Bangladesh Academy of Sciences, Vol. 32, No. 1, 71-77, 2008

scholarly journals More on the cardinality of a topological space

2018 ◽  
Vol 19 (2) ◽  
pp. 269 ◽  
Author(s):  
M. Bonanzinga ◽  
N. Carlson ◽  
M. V. Cuzzupè ◽  
D. Stavrova
Keyword(s):  
Hausdorff Space ◽  
Negative Answer ◽  
Topological Spaces ◽  
Compact Sets ◽  
Hausdorff Spaces ◽  
Separation Axioms ◽  
Covering Properties ◽  
Previous Inequality ◽  
The Impact ◽  
The Continuum

<p>In this paper we continue to investigate the impact that various separation axioms and covering properties have onto the cardinality of topological spaces. Many authors have been working in that field. To mention a few, let us refer to results by Arhangel’skii, Alas, Hajnal-Juhász, Bell-Gisburg-Woods, Dissanayake-Willard, Schröder and to the excellent survey by Hodel “Arhangel’skii’s Solution to Alexandroff’s problem: A survey”.</p><p>Here we provide improvements and analogues of some of the results obtained by the above authors in the settings of more general separation axioms and cardinal invariants related to them. We also provide partial answer to Arhangel’skii’s question concerning whether the continuum is an upper bound for the cardinality of a Hausdorff Lindelöf space having countable pseudo-character (i.e., points are Gδ). Shelah in 1978 was the first to give a consistent negative answer to Arhangel’skii’s question; in 1993 Gorelic established an improved result; and further results were obtained by Tall in 1995.  The question of whether or not there is a consistent bound on the cardinality of Hausdorff Lindelöf spaces with countable pseudo-character is still open. In this paper we introduce the Hausdorff point separating weight Hpw(X), and prove that (1) |X| ≤ Hpsw(X)<sup>aL</sup><sup>c</sup><sup>(X)ψ(X)</sup>, for Hausdorff spaces and (2) |X| ≤ Hpsw(X)<sup>ω</sup><sup>L</sup><sup>c</sup><sup>(X)ψ(X)</sup>, where X is a Hausdorff space with a π-base consisting of compact sets with non-empty interior. In 1993 Schröder proved an analogue of Hajnal and Juhasz inequality |X| ≤ 2<sup>c(X)χ(X)</sup> for Hausdorff spaces, for Urysohn spaces by considering weaker invariant - Urysohn cellularity Uc(X) instead of cellularity c(X). We introduce the n-Urysohn cellularity n-Uc(X) (where n≥2) and prove that the previous inequality is true in the class of n-Urysohn spaces replacing Uc(X) by the weaker n-Uc(X). We also show that |X| ≤ 2<sup>Uc(X)πχ(X)</sup> if X is a power homogeneous Urysohn space.</p>

Sign in / Sign up

Export Citation Format

Share Document