On Fuzzy L-paracompact Topological Spaces

Fuzzy Sets and Systems, 1997

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.

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

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

Fuzzy Sets and Systems, 2002

The concepts of P-compactness, countable P-compactness, the P-Lindelöf property are introduced in L-topological spaces by means of preopen L-sets and their inequalities when L is a complete DeMorgan algebra. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required. They can also be characterized by means of preclosed L-sets and their inequalities. Their properties are researched. Further when L is a completely distributive DeMorgan algebra, their many characterizations are presented.

In this paper we have obtained some results on fuzzy supra topological spaces introduced in [9].

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.

Recently, the author [25] introduced a new class spaces namely, soft nearly paracompact spaces and established some characterizations of these spaces. In this work, some new notions in soft space such as soft -almost regular spaces, soft almost paracompact spaces and soft -almost paracompact spaces are introduced. We also investigate some basic properties of these concepts and obtain several interesting results and characterizations of soft nearly compact and nearly paracompact 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.

Techno Sky Publications, 2021

The purpose of this article is to study the concepts of fuzzy paraopen and fuzzy paraclosed sets in fuzzy topological spaces Further, we introduce few class of fuzzy maps namely fuzzy paracontinuous, *-fuzzy paracontinuous, fuzzy parairresolute, fuzzy minimal paracontinuous, fuzzy maximal paracontinuous mappings and study their prpoerties.

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.

Chaos, Solitons & Fractals, 2005

In this paper, we introduce and study the notion of h-compactness for fuzzy topological spaces.

Journal of Mathematical Analysis and Applications, 1988

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.

2024

An interesting area of research in topology is D-paracompact spaces. It is a significant type of topological spaces that retain compactness while benefiting from paracompactness, which is considered a generalisation of compact spaces. The concept of D-paracompactness was introduced, and its basic characteristics were examined by the author in [18]. In this research, we introduce and improve this concept further by using a special type of covering and the difference sets (called D-sets), which contain new and impact properties. As a result, we obtained several new properties and results. We discuss the concept, characteristics, and theorems that related of D-paracompact space. We also studied different characterizations of D-paracompact spaces and discussed how they relate to other topological characteristics. We also give numerous instances of D-paracompact spaces along with highlighting their applicability in different topological spaces.

International Journal of Mathematics and Mathematical Sciences, 1997

Letnandmbe infinite cardinals withn≤mandnbe a regular cardinal. We prove certain implications of[n,m]-strongly paracompact,[n,m]-paracompact and[n,m]-metacompact spaces. LetXbe[n,∞]-compact andYbe a[n,m]-paracompact (resp.[n,∞]-paracompact),Pn-space (resp.wPn-space). Ifm=∑k<nmkwe prove thatX×Yis[n,m]-paracompact (resp.[n,∞]-paracompact