On compactness of induced I(L)-fuzzy topological spaces
Yixiang Chen1997, Fuzzy Sets and Systems
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
The induced I(L)-fuzzy topological spaces for L-fuzzy topological spaces introduced by Wang Geping is a kind of important fuzzy topological space. In this paper, the author studies the fuzzy compactness of induced I(L)-fuzzy topological spaces. Some available relations between molecular nets of an L-fuzzy topological space and that of its induced I(L)-fuzzy topological space are firstly presented. By using these relations, the author obtains that the induced l(L)-fuzzy topological space is strong fuzzy compact (resp. fuzzy compact, N-compact) if and only if the L-fuzzy topological space is strong fuzzy compact (resp. fuzzy compact, N-compact). The author also proves that the induced l(L)-fuzzy topological space is •-paracompact if and only if the L-fuzzy topological space is ,-paracompact. (~) 1997 Elsevier Science B.V.
Related papers
Compactness in fuzzy topological spaces
Journal of Mathematical Analysis and Applications, 1978
Since earlier approaches to compactness in fuzzy spaces have serious limitations, we propose a new definition of fuzzy space compactness. In doing so, we observe that it is possible to have degrees of compactness, which we call acompactness (a a member of a designated lattice). We obtain a Tychonoff Theorem for an arbitrary product of or-compact fuzzy spaces and a l-point compactification. We prove that the fuzzy unit interval is tx-compact. Compact fuzzy topological spaces were first introduced in the literature by Chang [l] who proved two results about such spaces. The next compactness results, due to Goguen [2], are an Alexander Subbase Theorem and a Tychonoff Theorem for finite products. Goguen was the first to point out a deficiency in Chang's compactness theory by showing that the Tychonoff Theorem is false for infinite products. Although Wong [8] treats compactness, his results are not significant. Weiss deals with a subfamily of the family of all fuzzy topologies on a fixed set. Since no member of Weiss' subfamily is compact in the sense of Chang, Weiss introduced a new notion of compactness applicable only to his subfamily. Lowen [4] gave a new definition of a compact fuzzy space which, when restricted to Weiss' subfamily, is equivalent to Weiss' notion. However, Lowen is able to obtain only a finite Tychonoff Theorem. In a second paper [5], Lowen gives a different definition of a compact fuzzy space and drastically alters the definition of a fuzzy topological space. Although
On compact and semicompact fuzzy soft topological spaces
2014
The concept of compactness is one of the central and important concepts of paramount interest to topologists and it seems to be the most celebrated type among all the covering properties. In this paper the concept of compactness of fuzzy soft topological spaces is introduced and characterized in terms of finite intersection property (FIP) and in terms of fuzzy soft mappings. This concept is also generalized by introducing the concept of fuzzy soft semi-compact topological spaces. Invariance of the property under suitable maps is also taken into consideration.
Some more results on induced fuzzy topological spaces
Fuzzy Sets and Systems, 1998
The concept of induced fuzzy topological space, introduced by Weiss [J. Math. Anal. Appl. 50 (1975) 142 150], was defined with the notions of a lower semi-continuous function.
On Compactness in Fuzzy Soft Topological Spaces
In this Paper, we introduce a new definition of the cover so-called fuzzy soft p-cover. According to this notion, we define a new type of compactness in fuzzy soft topology so-called p *-compactness which is extension to Kandil's compactness in the fuzzy topology [7] and is avoid some Chang's deviations in the fuzzy and fuzzy soft topology [4]. Some of their basic results, properties and relations are investigated with some necessary examples.
On Fuzzy I b -compact Spaces and Fuzzy I b -closed Spaces
This paper deals with the concept of fuzzy I b-compactness in the generalized setting of a fuzzy topological space X. The concept of fuzzy b-compact topological space was introduced by G. Balasubramanian in 1997. Fuzzy I b-compactness is shown to be a generalization of the concept of fuzzy b-compactness. Fuzzy filter-base (ffb) is used to characterize the said concept to some extent. Concept of-I FIP (finite intersection property modulo I) is used to characterize and study I b-compactness for fuzzy topological spaces. Restriction of the notion of fuzzy I b-compactness to the arbitrary fuzzy sets in X and invariance of the property under suitable maps are also taken into consideration. The concept of fuzzy I b-closed spaced is also introduced.
Some more results on completely induced fuzzy topological spaces
Fuzzy Sets and Systems, 1992
The object of the paper is to present some new results on completely induced fuzzy topological spaces and completely semi-induced spaces earlier introduced by the authors in this journal. When a fuzzy topological space becomes a completely induced space is discussed. Examples of completely induced space are also cited. Now we cite two examples of these spaces. Example 1. Let (X, rl) be an indiscrete 0165-0114/92/$05.00
On Fuzzy L-paracompact Topological Spaces
AIP Proceedings
The aim of this paper is to study fuzzy extensions of some covering properties defined by L. Kalantan as a modification of some kinds of paracompactness-type properties due to A.V.Arhangel'skii and studied later by other authors.
On (L,M)-fuzzy soft topological spaces
Journal of Mathematical and Computational Science, 2017
In this paper, the concepts of (L,M)-fuzzy soft topological spaces, (L,M)-fuzzy soft base and (L,M)-fuzzy soft filter spaces were introduced and their properties were studied, where L be a completely distributive lattice with 0 and 1 elements and M be a strictly two-sided, commutative quantale lattice. Also, the relationships between these concepts were investigated.
On -N-Topological Spaces Associated with Fuzzy Topological Spaces
This paper deals with the concept of-limit points of crisp subsets of a fuzzy topological space and the concept of-closed sets in. A special type of crisp subsets (termed as-N-open sets) of a fuzzy topological space is defined as the complement of-closed sets in and a special class of ordinary topological spaces is introduced. This newly defined graded topological spaces (denoted by (N)) are used to study and characterize some fuzzy topological properties such as compactness and other compact-like covering properties and Hausdorffness, connectedness etc.
C*-compactness in L-Fuzzy Topological Spaces
In this paper we introduce stronger form of the notion of cover so-called p-cover which is more appropriate. According to this cover we introduce and study another type of compactness in L-fuzzy topology so-called C*-compact and study some of its properties with some interrelation.
More on Fuzzy Topological Spaces on Fuzzy Space
International Journal of Fuzzy Systems and Advanced Applications, 2021
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
On Compactness and Connectedness of Invertible Fuzzy Topological Spaces
2012
In this paper we study the effect of invertibility on compactness and connectedness of a fuzzy topological space. We have obtained certain conditions for an invertible fuzzy topological space to be compact and fuzzy connected. If the invertible subspace is compact, then it is proved that the parent fuzzy topological space is also compact. It is also proved that in a type 2 completely invertible fuzzy topological space, fuzzy connectedness and fuzzy super connectedness are same. AMS Subject Classification: 54A40
On Some New Types of Fuzzy Soft Compact Spaces
2023
In this article, we apply the concept of fuzzy soft δ-open sets to defne new types of compactness in fuzzy soft topological spaces, namely, δ-compactness and δ *-compactness. We explore some of their basic properties and reveal the relationships between these types and that which are defned by other authors. Also, we show that δ *-compactness is more general than that which is presented in other papers. To clarify the obtained results and relationships, some illustrative examples are given.
An Introduction to Fuzzy Topological Spaces
Advances in Pure Mathematics, 2021
Topology has enormous applications on fuzzy set. An attention can be brought to the mathematicians about these topological applications on fuzzy set by this article. In this research, first we have classified the fuzzy sets and topological spaces, and then we have made relation between elements of them. For expediency, with mathematical view few basic definitions about crisp set and fuzzy set have been recalled. Then we have discussed about topological spaces. Finally, in the last section, the fuzzy topological spaces which is our main object we have developed the relation between fuzzy sets and topological spaces. Moreover, this article has been concluded with the examination of some of its properties and certain relationships among the closure of these spaces.
On fuzzy compact-open topology
Fuzzy Sets and Systems, 1996
The concept of fuzzy compact-open topology is introduced and some characterizations of this topology are discussed.
Some Universal Constructions For I- Fuzzy Topological Spaces
Journal of Advances in Mathematics, 2014
has introduced the concept of I-fuzzy topological spaces (X, μ, F) where X is an ordinary set, μ is a fuzzy set in X and F is a family of fuzzy sets in X satisfying some axioms. In this paper we introduce universal constructions, namely, fuzzy products, fuzzy equalizers and fuzzy pullbacks for I-fuzzy topological spaces. Also we discuss some results concerning all such universal objects.
A new category for fuzzy topological spaces
Fuzzy Sets and Systems, 1992
A new category for fuzzy topological spaces is defined that includes some important categories proposed so far. A new category for fuzzy sets is also proposed.
On Some Structural Properties of Fuzzy Soft Topological Spaces
2013
This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft closure and fuzzy soft interior of a fuzzy soft set are studied and investigated. Fuzzy soft exterior and fuzzy soft boundary of a fuzzy soft set are introduced and some properties related to these structures are established.
A new approach towards characterization of semicompactness of fuzzy topological space and its crisp subsets
Journal of Fuzzy Set Valued Analysis, 2013
It is widely accepted that one of the most satisfactory generalization of the concept of compactness to fuzzy topological spaces is α−compactness, first introduced by Gantner et al. in 1978, followed by further investigations by many others. Chakraborty et al. introduced fuzzy semicompact set and investigated and characterized fuzzy semicompact spaces in terms of fuzzy nets and fuzzy pre f ilterbases in 2005. In this paper, we propose to introduce a new approach to characterize the notion of α−semicompactness in terms of ordinary nets and f ilters. This paper deals also with the concept of α−semilimit points of crisp subsets of a fuzzy topological space X and the concept of α−semiclosed sets in X and these concepts are used to define and characterize α−semicompact crisp subsets of X.
Generalized Fuzzy Topological Spaces
2012
We introduce the concepts of generalized fuzzy topological spaces, generalized fuzzy neighborhood systems, in Sostak sense. Furthermore, we construct generalized fuzzy interior, generalized fuzzy closure on generalized fuzzy topological space and generalized fuzzy neighborhood system. Also, we introduce the concepts of generalized fuzzy () , y y ¢-continuous. We study their properties and discuss the relationships between these concepts.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.