scholarly journals Characterized Fuzzy R2.5 and Characterized Fuzzy T3.5 Spaces

2017 ◽  
Vol 13 (1) ◽  
pp. 7048-7073
Author(s):  
Ahmed Saeed Abd-Allah
Keyword(s):  
Topological Space ◽  
Tychonoff Space ◽  
Proximity Space ◽  
Completely Regular ◽  
Fuzzy Function ◽  
Continuous Mappings ◽  
Fuzzy Space ◽  
Fuzzy Topological Space ◽  
The Given ◽  
Proximity Spaces

This paper, deals with, introduce and study the notions of haracterized fuzzy R2.5 spaces and of characterized fuzzy T3.5 spaces by using the notion of fuzzy function family presented in [21] and the notion of φ1,2ψ1,2-fuzzy continuous mappings presented in [5] as a generalization of all the weaker and stronger forms of the fuzzy completely regular spaces introduced in [11,24,26,29]. We denote by characterized fuzzy T3.5 space or characterized fuzzy Tychonoff space to the characterized fuzzy space which is characterized fuzzy T1 and characterized fuzzy R2.5 space in this sense. The relations between the characterized fuzzy T3.5 spaces, the characterized fuzzy T4 spaces and the characterized fuzzy T3 spaces are introduced. When the given fuzzy topological space is normal, then the related characterized fuzzy space is finer than the associated characterized fuzzy proximity space which is presented in [1]. Moreover, the associated characterized fuzzy proximity spaces and the characterized fuzzy T4 spaces are identical with help of the complementarilysymmetric fuzzy topogenous structure, that is, identified with the fuzzy proximity δ. More generally, the fuzzy function family of all φ1,2ψ1,2-fuzzy continuous mappings are applied to show that the characterized fuzzy R2.5 spaces and the associated characterized fuzzy proximity spaces are identical.

Separating Closed Sets by Continuous Mappings into Developable Spaces

1981 ◽  
Vol 33 (6) ◽  
pp. 1420-1431 ◽  
Author(s):  
Harald Brandenburg
Keyword(s):  
Topological Space ◽  
Double Sequence ◽  
Completely Regular ◽  
Closed Sets ◽  
Continuous Mappings ◽  
Neighbourhood Base ◽  
Image Position ◽  
Metrizable Spaces ◽  
Metrization Theorem ◽  
Developable Spaces

A topological space X is called developable if it has a development, i.e., a sequence of open covers of X such that for each x ∈ X the collection is a neighbourhood base of x, whereThis class of spaces has turned out to be one of the most natural and useful generalizations of metrizable spaces [23]. In [4] it was shown that some well known results in metrization theory have counterparts in the theory of developable spaces (i.e., Urysohn's metrization theorem, the Nagata-Smirnov theorem, and Nagata's “double sequence theorem”). Moreover, in [3] it was pointed out that subspaces of products of developable spaces (i.e., D-completely regular spaces) can be characterized in much the same way as subspaces of products of metrizable spaces (i.e., completely regular T1-spaces).

scholarly journals Compactness in intuitionistic fuzzy topological spaces

2005 ◽  
Vol 2005 (1) ◽  
pp. 19-32 ◽  
Author(s):  
A. A. Ramadan ◽  
S. E. Abbas ◽  
A. A. Abd El-Latif
Keyword(s):  
Topological Space ◽  
Continuous Mapping ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Continuous Mappings ◽  
Weakly Continuous ◽  
Fuzzy Topological Space ◽  
Definition Of ◽  
Fuzzy Topological Spaces ◽  
Almost Continuous

We introduce fuzzy almost continuous mapping, fuzzy weakly continuous mapping, fuzzy compactness, fuzzy almost compactness, and fuzzy near compactness in intuitionistic fuzzy topological space in view of the definition of Šostak, and study some of their properties. Also, we investigate the behavior of fuzzy compactness under several types of fuzzy continuous mappings.

scholarly journals Homogeneous Components of a CDH Fuzzy Space

2019 ◽  
Vol 9 (4) ◽  
pp. 2691
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Font Size ◽  
Fuzzy Space ◽  
Fuzzy Topological Space

<span style="font-size: medium;"><span style="font-size: medium;"><span style="font-size: 10px;">We prove that fuzzy homogeneous components of a CDH fuzzy topological space  (X,T) are clopen and also they are CDH topological subspaces of its 0-cut topological space (X,T0).</span><br /></span></span><span style="font-size: medium;">   </span>

scholarly journals New Concepts of Dense set in i-Topological space and Proximity Space

2021 ◽  
Vol 12 (1S) ◽  
pp. 685-690
Author(s):  
Yiezi Kadham Mahdi AL Talkany, Et. al.
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Proximity Space ◽  
New Concepts ◽  
Proximity Spaces ◽  
Dense Set

A new kind of some topological spaces concepts has been defined in i-topological spaces with respect to proximity spaces in our paper.

scholarly journals Fuzzy Almost Generalized E-Continuous Mappings in Smooth Topological Spaces

2019 ◽  
Vol 8 (10S) ◽  
pp. 138-141 ◽  
Keyword(s):  
Topological Space ◽  
Compact Space ◽  
Continuous Mapping ◽  
Regular Space ◽  
Topological Spaces ◽  
Continuous Mappings ◽  
Fuzzy Topological Space ◽  
Index Terms ◽  
Almost Continuous

We introduce and study several interesting properties of fuzzy almost generalized e -continuous mappings in smooth topological spaces with counter examples. We also introduce fuzzy r - 1 2 fT e -space, r -fuzzy ge -space, r -fuzzy regular ge -space and r -fuzzy generalized e -compact space. It is seen that a fuzzy almost generalized e -continuous mapping, between a fuzzy r - 1 2 fT e -space and a fuzzy topological space, becomes fuzzy almost continuous mapping. Index Terms: fage -continuous, r - fge -space, r - fge -regular space, r - 1 2 fT e -space.

scholarly journals Fuzzy Semi Pre Homeomorphism in Fuzzy Topological Spaces

2020 ◽  
Vol 33 (4) ◽  
pp. 73
Author(s):  
Saleem Y. Majeed
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
New Class ◽  
Fuzzy Function ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces ◽  
Class Of Functions

   The aim of this paper is to introduce and study new class of fuzzy function called fuzzy semi pre homeomorphism in a fuzzy topological space by utilizing fuzzy semi pre-open sets. Therefore, some of their characterization has been proved; In addition to that we define, study and develop corresponding to new class of fuzzy semi pre homeomorphism in fuzzy topological spaces using this new class of functions.

scholarly journals More on Fuzzy Topological Spaces on Fuzzy Space

2021 ◽  
Vol 8 ◽  
pp. 21-26
Author(s):  
Abd Ulazeez Alkouri ◽  
Mohammad Hazaimeh ◽  
Ibrahim Jawarneh
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Separation Axioms ◽  
Fuzzy Space ◽  
Different Types ◽  
Fuzzy Topological Space ◽  
Isolated Points ◽  
Fuzzy Topological Spaces ◽  
Fuzzy Subsets

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of fuzzy spaces. Dip’s approach helps to rectify the deviation in some definitions of fuzzy subsets in fuzzy topological spaces. In this paper, further definitions, and theorems on fuzzy topological space fill the lack in Dip’s article. Different types of fuzzy topological space on fuzzy space are presented such as co-finite, co-countable, right and left ray, and usual fuzzy topology. Furthermore, boundary, exterior, and isolated points of fuzzy sets are investigated and illustrated based on fuzzy spaces. Finally, separation axioms are studied on fuzzy spaces

scholarly journals Intuitionistic fuzzy semi-generalized irresolute mappings

2011 ◽  
Vol 42 (2) ◽  
pp. 119-134
Author(s):  
Rathinasamy Santhi ◽  
K. Arun Prakash
Keyword(s):  
Topological Space ◽  
Intuitionistic Fuzzy ◽  
Continuous Mappings ◽  
Fuzzy Topological Space

The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy semi-generalized continuous mappings and intuitionistic fuzzy semi-generalized irresolute mappings in intuitionistic fuzzy topological space.

scholarly journals Separation Axioms in Intuitionistic Fuzzy Topological Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Amit Kumar Singh ◽  
Rekha Srivastava
Keyword(s):  
Topological Space ◽  
Left Adjoint ◽  
Topological Spaces ◽  
Intuitionistic Fuzzy ◽  
Separation Axioms ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

In this paper we have studied separation axiomsTi,i=0,1,2in an intuitionistic fuzzy topological space introduced by Coker. We also show the existence of functorsℬ:IF-Top→BF-Topand𝒟:BF-Top→IF-Topand observe that𝒟is left adjoint toℬ.

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