scholarly journals Fuzzy Ideal Supra Topological Spaces

2020 ◽  
Author(s):  
Fadhil Abbas
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Basic Structure ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Local Function ◽  
Closed Sets ◽  
Fuzzy Ideal ◽  
Neighbourhood Structure

Abstract In this paper, we introduce the notion of fuzzy ideals in fuzzy supra topological spaces. The concept of a fuzzy s-local function is also introduced here by utilizing the s-neighbourhood structure for a fuzzy supra topological space. These concepts are discussed with a view to nd new fuzzy supra topologies from the original one. The basic structure, especially a basis for such generated fuzzy supra topologies and several relations between different fuzzy ideals and fuzzy supra topologies are also studied here. Moreover, we introduce a fuzzy set operator ΨS and study its properties. Finally, we introduce some sets of fuzzy ideal supra topological spaces (fuzzy *-supra dense-in-itself sets, fuzzy S*-supra closed sets, fuzzy *-supra perfect sets, fuzzy regular-I-supra closed sets, fuzzy-I-supra open sets, fuzzy semi-I-supra open sets, fuzzy pre-I-supra open sets, fuzzy α-I-supra open sets, fuzzy β-I-supra open sets) and study some characteristics of theses sets and then we introduce some fuzzy ideal supra continuous functions.

scholarly journals Fuzzy Ideal Supra Topological Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Fadhil Abbas
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Basic Structure ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Local Function ◽  
Fuzzy Ideal ◽  
Neighbourhood Structure

In this paper, we introduce the notion of fuzzy ideals in fuzzy supra topological spaces. The concept of a fuzzy s-local function is also introduced here by utilizing the s-neighbourhood structure for a fuzzy supra topological space. These concepts are discussed with a view to find new fuzzy supra topologies from the original one. The basic structure, especially a basis for such generated fuzzy supra topologies, and several relations between different fuzzy ideals and fuzzy supra topologies are also studied here. Moreover, we introduce a fuzzy set operator Ψ S and study its properties. Finally, we introduce some sets of fuzzy ideal supra topological spaces (fuzzy ∗ -supra dense-in-itself sets, fuzzy S ∗ -supra closedsets, fuzzy ∗ -supra perfect sets, fuzzy regular-I-supra closedsets, fuzzy-I-supra opensets, fuzzy semi-I-supra opensets, fuzzy pre-I-supra opensets, fuzzy α -I-supra opensets, and fuzzy β -I-supra opensets) and study some characteristics of these sets, and then, we introduce some fuzzy ideal supra continuous functions.

scholarly journals Fine Fuzzy sp Closed Sets in Fine Fuzzy Topological Spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 1306-1313
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Inverse Image ◽  
Continuous Functions ◽  
Topological Spaces ◽  
The Novel ◽  
Closed Set ◽  
Closed Sets ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The main view of this article is the extended version of the fine topological space to the novel kind of space say fine fuzzy topological space which is developed by the notion called collection of quasi coincident of fuzzy sets. In this connection, fine fuzzy closed sets are introduced and studied some features on it. Further, the relationship between fine fuzzy closed sets with certain types of fine fuzzy closed sets are investigated and their converses need not be true are elucidated with necessary examples. Fine fuzzy continuous function is defined as the inverse image of fine fuzzy closed set is fine fuzzy closed and its interrelations with other types of fine fuzzy continuous functions are obtained. The reverse implication need not be true is proven with examples. Finally, the applications of fine fuzzy continuous function are explained by using the composition.

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.

scholarly journals Locally closed sets andLC-continuous functions

1989 ◽  
Vol 12 (3) ◽  
pp. 417-424 ◽  
Author(s):  
M. Ganster ◽  
I. L. Reilly
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Closed Set ◽  
Closed Sets ◽  
Generalized Continuity ◽  
Locally Closed Sets ◽  
Nearly Continuous

In this paper we introduce and study three different notions of generalized continuity, namely LC-irresoluteness, LC-continuity and sub-LC-continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a topological space X is locally closed if it is the intersection of an open and a closed set. We discuss some properties of these functions and show that a function between topological spaces is continuous if and only if it is sub-LC-continuous and nearly continuous in the sense of Ptak. Several examples are provided to illustrate the behavior of these new classes of functions.

scholarly journals On β-local Functions in Ideal topological Spaces

2020 ◽  
Vol 13 (4) ◽  
pp. 758-765
Author(s):  
Pournima Powar ◽  
Takashi Noiri ◽  
Shikha Bhadauria
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Local Function ◽  
Closed Sets ◽  
Local Functions

In this paper, by using β-open sets in [1] we introduce and investigate the conceptsof the β-local function, Is∗g-β-closed sets and Ig-β-closed sets in an ideal topological space. In addition to the properties, an operation cl∗β is defined and the properties are obtained similarly with the local function in [8].

scholarly journals A Tychonoff theorem in intuitionistic fuzzy topological spaces

2004 ◽  
Vol 2004 (70) ◽  
pp. 3829-3837
Author(s):  
Doğan Çoker ◽  
A. Haydar Eş ◽  
Necla Turanli
Keyword(s):  
Topological Space ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Tychonoff Theorem

The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some characterizations concerning fuzzy compactness. Lastly we give a Tychonoff-like theorem.

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 Topological Games on Product Spaces and its Fuzzification

2013 ◽  
Vol 2 ◽  
pp. 11-15
Author(s):  
Bidyanand Prasad ◽  
BP Kumar
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Perfect Information ◽  
Topological Spaces ◽  
Product Spaces ◽  
Pursuit And Evasion

This paper is concerned with the introduction of an infinite positional game of pursuit and evasion over an ideal of a topological space. A topological game has been played over some new D-product and C-product spaces of two Hausdorff topological spaces. Perfect information, decisions and goals in a game may not be feasible. Hence, fuzzy set theory has been applied in this paper to obtain better results. Academic Voices, Vol. 2, No. 1, 2012, Pages 11-15 DOI: http://dx.doi.org/10.3126/av.v2i1.8278

Neutrosophic Nano Ideal Topological Structures

2018 ◽  
Author(s):  
Parimala Mani ◽  
Karthika M ◽  
jafari S ◽  
Smarandache F ◽  
Ramalingam Udhayakumar
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Structures ◽  
Basic Properties ◽  
Closed Sets ◽  
Structural Space ◽  
New Type

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutrosophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

scholarly journals Constructing Banaschewski compactification without Dedekind completeness axiom

2004 ◽  
Vol 2004 (69) ◽  
pp. 3799-3816
Author(s):  
S. K. Acharyya ◽  
K. C. Chattopadhyay ◽  
Partha Pratim Ghosh
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Open Problems ◽  
Structure Space ◽  
Ordered Field ◽  
Completeness Axiom ◽  
Dedekind Completeness ◽  
Stone Theorem ◽  
Stone’S Theorem

The main aim of this paper is to provide a construction of the Banaschewski compactification of a zero-dimensional Hausdorff topological space as a structure space of a ring of ordered field-valued continuous functions on the space, and thereby exhibit the independence of the construction from any completeness axiom for an ordered field. In the process of describing this construction we have generalized the classical versions of M. H. Stone's theorem, the Banach-Stone theorem, and the Gelfand-Kolmogoroff theorem. The paper is concluded with a conjecture of a split in the class of all zero-dimensional but not strongly zero-dimensional Hausdorff topological spaces into three classes that are labeled by inequalities between three compactifications ofX, namely, the Stone-Čech compactificationβX, the Banaschewski compactificationβ0X, and the structure space𝔐X,Fof the lattice-ordered commutative ringℭ(X,F)of all continuous functions onXtaking values in the ordered fieldF, equipped with its order topology. Some open problems are also stated.

Sign in / Sign up

Export Citation Format

Share Document