首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 424 毫秒
1.
In this paper, we construct a topological category of pretopological L-fuzzy Q-convergence spaces, which contains the category of topological L-fuzzy Q-convergence spaces as a bireflective full subcategory. Considering the connections with L-fuzzy topology, it is proved that the category of topological L-fuzzy Q-convergence spaces is isomorphic to the category of topological L-fuzzy quasi-coincident neighborhood spaces, and the latter is isomorphic to the category of L-fuzzy topological spaces. Moreover, we find that our pretopological L-fuzzy Q-convergence spaces can be characterized as a kind of L-fuzzy quasi-coincident neighborhood spaces, which is called strong L-fuzzy quasi-coincident neighborhood space.  相似文献   

2.
This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [1]. It investigates topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by ?ukasiewicz logic in [0, 1]) . The concept of α-irresolute functions and α-compactness in the framework of fuzzifying topology are introduced and some of their properties are obtained. We use the finite intersection property to give a characterization of fuzzifying α-compact spaces. Furthermore, we study the image of fuzzifying α-compact spaces under fuzzifying α-continuity and fuzzifying α-irresolute maps.  相似文献   

3.
This paper is a continuation of [1]. That is, it considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [2]. It investigates topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0, 1]). Other characterizations of fuzzifying α-compactness are given, including characterizations in terms of nets and α-subbases. Several characterizations of locally α-compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.  相似文献   

4.
首先引入了直觉Fuzzifying邻域系和直觉Fuzzifying邻域空间的概念,进而证明了直觉Puzzifying邻域空间范畴IFYNS同构于直觉Fuzzifying拓扑空间范畴IFYTOP.  相似文献   

5.
On Q-sobriety     
The study of fixed-basis variety-based topology was initiated by S.A. Solovyov (in 2008), which, among other things, generalizes fuzzy topology. We extend within this framework, an earlier result due to Srivastava et al. (in 1998), which showed that the category of sober fuzzy topological spaces is the epireflective hull of the fuzzy Sierpinski space in the category of T0-fuzzy topological spaces.  相似文献   

6.
L-fuzzy sets and, subsequently, L-fuzzy topological spaces are considered in this paper, where L is a complete and completely distributive non-atomic Boolean algebra. A few separation properties as well as subspace L-fuzzy topology are defined here, in the light of an earlier paper. These are more similar to ordinary topological spaces than to fuzzy topological spaces.  相似文献   

7.
《Quaestiones Mathematicae》2013,36(2):203-207
Abstract

Following a lead given by I.W. Alderton, it is shown that the MacNeille completion and the universal initial completion coincide for the categories of zero-dimensional fuzzy T0-topological spaces, T0-fuzzy closure spaces, 2T 0-fuzzy bitopological spaces, and T 1-fuzzy topological spaces and that these turn out to be respectively the categories of zero-dimensional fuzzy topological spaces, fuzzy closure spaces, fussy bitopological spaces, and fuzzy R 0 topological spaces.  相似文献   

8.
Given an arbitrary connected topological space, an L-fuzzy space is constructed. When the original space is the real line (unit interval) the constructed space is the L-fuzzy real line (L-fuzzy unit interval). For some spaces, including Rn for all n, the original space is embedded as a subspace of the constructed space. Lastly, the construction yields a non-trivial fuzzy topology on certain classically important spaces of monotone mappings.  相似文献   

9.
Editorial     
A new proof of the Katêtov-Tong Insertion Theorem for L-fuzzy topological spaces is given. All the proofs are performed in such a way that the presented results hold true in the more general case in which L-fuzzy topologies are replaced by σ-additive rings of L-fuzzy subsets.  相似文献   

10.
Directed spaces are the objects of study within directed algebraic topology. They are characterised by spaces of directed paths associated to a source and a target, both elements of an underlying topological space. The algebraic topology of these path spaces and their connections are studied from a categorical perspective. In particular, we study the preorder category associated to a directed space and various “quotient” categories arising from algebraic topological functors. Furthermore, we propose and study a new notion of directed homotopy equivalence between directed spaces.   相似文献   

11.
Considering complete Boolean algebras G as sets of truth values a new concept of compactness—so-called probabilistic compactness — is introduced to G-fuzzy topological spaces. The aim of this paper is to show that the most important theorems of the theory of ordinary compact spaces remain true; e.g. probabilistic compactness is preserved under projective limits, every probabilistic compact space has an unique G-fuzzy uniformity being compatible with the underlying G-fuzzy topology, etc. Finally using the selection theorem due to Kuratowski and Ryll-Nardzewski a non-trivial example of a probabilistic compact space is given.  相似文献   

12.
Given an M-valued equality E: X×XM on a set X, we extend it to the M-valued equality ε: L X × L X M on the L-powerset L X of X, where L is a complete sublattice of a GL-monoid M. As a result, we come to a category SET(M,L) whose objects are quadruples (X,E,L X , ε). This category serves as a ground category for the category L-TOP(M) of (L,M)-valued topological spaces and some of its subcategories, which are the main subject of this paper. In particular, as special cases, we obtain here Chang-Goguen, Lowen, Kubiak-Šostak, and some other known categories related to fuzzy topology. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 237–247, 2005.  相似文献   

13.
In this paper, by generalizing Höhle and ?ostak’s stratified L-fuzzy neighborhood system, the notion of stratified L-neighborhood tower space is introduced. Then by enriching a group structure on a stratified L-neighborhood tower space, the notion of stratified L-neighborhood tower group is proposed. It is proved that this notion can be regarded as a natural extension of stratified L-neighborhood group dis- cussed by Ahsanullah etal. Indeed, the category of stratified L-neighborhood tower groups includes the category of stratified L-neighborhood groups as a concretely reflective (resp., coreflective) full subcategory. Furthermore, it is shown that the group operations enrich a stratified L-neighborhood tower space to be topological (generally, stratified L-neighborhood tower space is not topological). This means that there is no di?erence between stratified L-neighborhood tower group and topologically stratified L-neighborhood tower group.  相似文献   

14.
In this paper, a characterization for an I(L)-topological space to be generated by a given co-tower of L-topological spaces is obtained. Moreover, the relationship between some properties of an I(L)-topological vector space generated by a co-tower of L-topological vector spaces and the corresponding properties of the given co-tower of L-topological vector spaces is investigated. Our results show that if an I(L)-topological vector space generated by a co-tower of L-topological vector spaces has some properties, such as local convexity and local boundedness, then all L-topological vector spaces in the co-tower also have the same properties. But the converse is incorrect even in the case of I-topological vector space generated by a co-tower of classical topological vector spaces. Finally, we supply a necessary and sufficient condition for an I(L)-topological vector space generated by a co-tower of L-topological vector spaces with some properties, such as local convexity and local boundedness, to have such properties too.  相似文献   

15.
首先引入了I-fuzzy远域系和I-fuzzy远域空间的概念,然后构造了I-fuzzy远域空间和它们的连续映射的范畴,将此记作I-FRN.并进一步证明了I-FRN同构于I-FTOP.  相似文献   

16.
In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of (normal) TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concept of L-fuzzy sets, the notion of ϑ-lower and T-upper L-fuzzy rough approximation operators with respect to an L-fuzzy set is introduced and some related properties are presented. Then a new algebraic structure called (normal) TL-fuzzy rough n-ary polygroup is defined and investigated. Also, the (strong) homomorphism of ϑ-lower and T-upper L-fuzzy rough approximation operators is studied.  相似文献   

17.
LetX andY beT 1 topological spaces andG(X, Y) the space of all functions with closed graph. Conditions under which the Fell topology and the weak Fell topology coincide onG(X,Y) are given. Relations between the convergence in the Fell topologyτF, Kuratowski and continuous convergence are studied too. Characterizations of a topological spaceX by separation axioms of (G(X, R), τF) and topological properties of (G(X, R), τF) are investigated.  相似文献   

18.
根据L-模糊拓扑自身的特点,在L-模糊拓扑空间中引入了内部度的定义,详细讨论了它的性质,提出了L-模糊拓扑上的内部算子的概念,论证了L-TFIN(拓扑的L-模糊内部空间和其上的连续映射构成的范畴)同构于L-FTOP(L-模糊拓扑空间和其上的连续映射构成的范畴).  相似文献   

19.
Summary In [6] we introduced and investigated the notions of fI -sets and fI -continuous functions in ideal topological spaces. In this paper, we investigate their further important properties.  相似文献   

20.
In this paper, the duality of κ-normed topological vector spaces X is defined and investigated, where X is over the field K = R, or K = C, or a non-Archimedean field. For such spaces, an analog of the Mackey-Arens theorem is proved. The conditional κ-normability of spaces L(X) of linear topological homeomorphisms of a locally convex κ-normed space X is studied, where the image of elements under the corresponding operations is in L(X). Cases where the κ-normability of a topological vector space implies its local convexity are investigated. Applications of κ-normed spaces for resolutions of differential equations and for approximations of functions in mathematical economics are given. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 52, Functional Analysis, 2008.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号