scispace - formally typeset
Search or ask a question
Journal Article•DOI•

On fuzzy compact-open topology

S. Dang1, A. Behera•
Government College1
24 Jun 1996-Fuzzy Sets and Systems (North-Holland)-Vol. 80, Iss: 3, pp 377-381
TL;DR: The concept of fuzzy compact-open topology is introduced and some characterizations of this topology are discussed.
About: This article is published in Fuzzy Sets and Systems.The article was published on 1996-06-24. It has received 6 citations till now. The article focuses on the topics: Extension topology & General topology.
Citations
More filters
Journal Article•DOI•
On fuzzy function spaces.

[...]

Gunther Jäger
01 Dec 1999-International Journal of Mathematics and Mathematical Sciences
TL;DR: This paper goes somewhat deeper in the investigation of fuzzy function spaces using the notion of splitting and conjoining structures on fuzzy subsets using the connection to the exponential law and gives several examples of such structures.
Abstract: In [3], we started the investigation of compactness in fuzzy function spaces in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. This paper goes somewhat deeper in the investigation of fuzzy function spaces using the notion of splitting and conjoining structures on fuzzy subsets. We discuss the connection to the exponential law and give several examples of such structures. As a special case, we study a notion of fuzzy compact open topology.

11 citations

Cites background from "On fuzzy compact-open topology"

  • ...In the meantime, three papers on this subject have appeared (Peng [11], Dang and Behera [2], and Alderton [1])....

    [...]

Journal Article•DOI•
Fuzzy topologies on function spaces

[...]

J. K. Kohli1, A. R. Prasannan2•
Hindu College, University of Delhi1, University of Delhi2
16 Dec 2000-Fuzzy Sets and Systems
TL;DR: This paper introduces and study three different fuzzy topologies on a given function space and investigates their applications to knowledge representation in discrete geometry.

5 citations

Journal Article•DOI•
Fuzzifying topologies on the space of linear operators

[...]

Cong-hua Yan1•
Nanjing Normal University1
01 Mar 2014-Fuzzy Sets and Systems
TL;DR: It is proved a sufficient and necessary condition for which the fuzzifying topologies are compatible with the structure on the space of linear operators, and the net convergence, fuzzy boundedness, and fuzzy continuity of evaluation mappings in the fuzzify topological linear space of pointwise convergence.

5 citations

Proceedings Article•DOI•
On F-homotopy and F-fundamental group

[...]

Eduardo Silva Palmeira1, Benjamin Bedregal2•
State University of Santa Cruz1, Federal University of Rio Grande do Norte2
18 Mar 2011
TL;DR: This work presents a formalization of the concept of homotopy considering the first point of view of fuzzy topological spaces, and investigates issues related tohomotopy, function spaces and fundamental group considering this point of points of view.
Abstract: In general, there are two main ways to define fuzzy topological spaces: (1) given a set X we can take a family of fuzzy subsets of X which satisfies special axioms of topology in X or (2) if τ is a topology at X in the usual sense and A is a fuzzy subset of X, we can consider the special family of fuzzy subsets τ∗ generated by τ in such way that (A, τ∗) is a fuzzy topological space. We present a formalization of the concept of homotopy considering the first point of view of fuzzy topological spaces. We start by maki ng a comparison between the definitions of fuzzy topological spaces in the sense of Morderson [16] and Gunduz [10], as well as their respective concepts of continuity. Furthermore, we investigate issues related to homotopy, function spaces and fundamental group considering this point of view of homotopy.

3 citations

Cites background from "On fuzzy compact-open topology"

  • ...4: (Dang [6]) Let X be a set and let U = {Ai : i ∈ K} be a family of subsets of X , with each Ai having a fuzzy topology....

    [...]

Journal Article•
Intuitionistic fuzzy exponential map via generalized open set

[...]

R. Dhavaseelan, E. Roja, M. K. Uma
01 Jan 2012-International Journal of Mathematical Archive
TL;DR: The concept of generalized intuitionistic fuzzy compact open topology is introduced and some characterization of this topology are discussed.
Abstract: The concept of generalized intuitionistic fuzzy compact open topology is introduced.Some characterization of this topology are discussed.
References
More filters
Book•
Fuzzy sets

[...]

Lotfi A. Zadeh
01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

52,705 citations

Journal Article•DOI•
Fuzzy topological spaces

[...]

C.L Chang1•
National Institutes of Health1
01 Oct 1968-Journal of Mathematical Analysis and Applications

1,997 citations

"On fuzzy compact-open topology" refers background in this paper

  • ...Ever since the introduction of fuzzy set by Zadeh [13] and fuzzy topological space by Chang [2], several authors have tried successfully to generalize numerous pivot concepts of general topology to the fuzzy setting....

    [...]

  • ...The concepts of fuzzy topologies are standard by now and can be referred from [2, 8, 13]....

    [...]

  • ...(Chang [2])....

    [...]

  • ...Preliminaries Ever since the introduction of fuzzy set by Zadeh [13] and fuzzy topological space by Chang [2], several authors have tried successfully to generalize numerous pivot concepts of general topology to the fuzzy setting....

    [...]

  • ...It is clear that {xt} x Y is fuzzy homeomorphic [2] to Y and hence {x,} x Y is fuzzy compact [9]....

    [...]

Journal Article•DOI•
Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence

[...]

Pu Pao-Ming1, Liu Ying-Ming1•
Sichuan University1
01 Aug 1980-Journal of Mathematical Analysis and Applications

995 citations

"On fuzzy compact-open topology" refers background in this paper

  • ...We need to find a fuzzy neighborhood [8] W of Xk such that f ( w ) <~ NK, v; this will suffice to prove f to be a fuzzy continuous map....

    [...]

  • ...For the definitions of fuzzy point and fuzzy neighborhood of a fuzzy point we refer to [8]....

    [...]

  • ...The concepts of fuzzy topologies are standard by now and can be referred from [2, 8, 13]....

    [...]

Journal Article•DOI•
On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity

[...]

K.K Azad1•
Allahabad University1
01 Jul 1981-Journal of Mathematical Analysis and Applications

430 citations

Journal Article•DOI•
Fuzzy vector spaces and fuzzy topological vector spaces

[...]

A.K Katsaras1, D.B Liu1•
State University of Campinas1
15 Mar 1977-Journal of Mathematical Analysis and Applications

255 citations

"On fuzzy compact-open topology" refers background in this paper

  • ...[] Definition 2.8 (Katsara and Lin [ 7 ]). The product of two fuzzy sets A and B in an fts (X, T) is defined as (A × B)(x, y)= min(A(x), B(y)) for all (x, y) e X × Y....

    [...]

Related Papers (5)
Topological structure of a fuzzy function space——the pointwise convergent topology and compact open topology

[...]

01 Jan 1984
Peng Y
On stratiform L -fuzzy topologies and their application

[...]

01 May 2001-Fuzzy Sets and Systems
Xingfang Zhang, Guangwu Meng, Yalin Zheng, Qingde Zhang 
Condition for a function space to be locally compact

[...]

01 Feb 1972
R. V. Fuller
On the Fuzzy Number Space with the Level Convergence Topology

[...]

06 Dec 2012-Journal of Function Spaces and Applications
Juan J. Font, A. Miralles, Manuel Sanchis
Fuzzy topology with respect to continuous lattices

[...]

01 Mar 1990-Fuzzy Sets and Systems
M. W. Warner