On the resolvability of locally connected spaces

We solve a problem of Padmavally about resolvability of locally connected spaces, in the case where the space under consideration is regular.

     

On fuzzy covering properties

The purpose of this paper is to introduce properties of the notion of α-compactness for fuzzy topological spaces. Moreover, α _c-compact spaces are introduced and properties of them are also discussed for fuzzy topological spaces.      

On countable connected locally connected almost regular Urysohn spaces

We construct connected, locally connected, almost regular, countable, Urysohn spaces. This answers a problem of G.X. Ritter. We show that there are 2^c such non-homeomorphic spaces. We also show that there are 2^c non-homeomorphic spaces which are further rigid. We discuss the group of homeomorphisms of such spaces.The following question was raised by G.X. Ritter: Does there exist a countable connected locally connected Urysohn space which is almost regular? We answer this question in the affirmative and in fact, show that not only are there as many as 2^c such spaces but that there are just as many rigid spaces with the same properties. Furthermore we show that every countable Urysohn space is a subspace of such a space. We also prove that every countable group is isomorphic to the group of autohomeomorphisms of some connected locally connected almost regular Urysohn space. Examples are given of groups of order c which can be represented in this manner.     

Dual affine-metrically connected spaces

In this paper we study the dual geometry of a normalized affinely connected space A _n,n . In particular, we consider the dual affine-metrically connected spaces \(\mathop M\limits^p _{n,n} \) induced by a nondegenerate normalization of an affine-metrically connected space M _n,n .     

On convergence theory in fuzzy topological spaces and its applications

In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the Q-relation and the Q-neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong Q-compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar to the one which exists between the convergence of filters and the convergence of nets in topological spaces.     

Controlled fuzzy metric spaces and some related fixed point results

In this paper, we introduce a new extension in the subject of fuzzy metric, called controlled fuzzy metric space. This notion is a generalization of fuzzy b‐metric space. Also, we prove a Banach‐type fixed point theorem and a new fixed point theorem for some self‐mappings satisfying fuzzy ψ ‐contraction condition that is more general than existing theorems. Furthermore, we establish some examples about our main results.     

On Segre's product of partial line spaces and spaces of pencils

In this paper we prove that every collineation of the Segre product of strongly connected partial line spaces is (up to permutation of indices) the product of collineations of its components (Thm. 1.10). Spaces of pencils are strongly connected, so the claim holds for Segre products of them (Thm. 1.14). In the second part we study the extendability of collineations of Segre products of spaces of pencils under some natural embeddings. Received 4 Mai 1998.     

On compactifications with path connected remainders

We prove that every separable and metrizable space admits a metrizable compactification with a remainder that is both path connected and locally path connected. This result answers a question of P. Simon.

     

On the determination of fuzzy topological spaces and fuzzy neighbourhood spaces by their level-topologies

In this paper we discuss the problem of the reconstruction of a fuzzy topological space or a fuzzy neighbourhood space from an a priori given family of level-topologies. Necessary and sufficient conditions for the existence of a solution are given, and it is proved that in the particular case of fuzzy neighbourhood spaces this solution is always unique.     

On connected factors inK 1,3-free graphs

A graph is said to beK _1,3-free if it contains noK _1,3 as an induced subgraph. It is shown in this paper that every 2-connectedK _1,3-free graph contains a connected [2,3]-factor. We also obtain that every connectedK _1,3-free graph has a spanning tree with maximum degree at most 3. This research is partially supported by the National Natural Sciences Foundation of China and by the Natural Sciences Foundation of Shandong Province of China.     

On concretely both reflective and coreflective subconstructs of Chang fuzzy topological spaces

In this paper, the concretely both reflective and coreflective subconstructs of the construct CFTS of Chang fuzzy topological spaces are characterized and their relationship to such subconstructs of stratified fuzzy topological spaces is investigated. Properties of a particular such subconstruct of CFTS, the construct of weak fuzzy neighborhood spaces, are discussed in detail. And it is proved that there exists exactly c such subconstructs between the subconstruct of weakly induced spaces and CFTS.     

On fuzzy metric spaces

In this paper we introduce the concept of a fuzzy metric space. The distance between two points in a fuzzy metric space is a non-negative, upper semicontinuous, normal and convex fuzzy number. Properties of fuzzy metric spaces are studied and some fixed point theorems are proved.     

关于Banach空间的强凸性

本文讨论强凸性、Ｌ－ｋＲ，ＬωＲ和（Ｇ）性质之间的关系，指出强凸性介于ＬωＲ和（Ｇ）性质之间，证明光滑的有（Ｇ）性质的Ｂａｎａｃｈ空间是强凸的，此外指出存在一个Ｂａｎａｃｈ空间Ｘ，它是ＬωＲ但对任意自然数ｋ，Ｘ不是Ｌ－ｋＲ．     

Hyperspaces of nowhere topologically complete spaces

It is proved that ifX is a connected locally continuumwise connected coanalytic nowhere topologically complete space, then the hyperspace 2 ^X of all nonempty compact subsets ofX is strongly universal in the class of all coanalytic spaces. Moreover, 2 ^X is homeomorphic to Π₂ ifX is a Baire space, and toQ∖Π₁ ifX contains a dense absoluteG _δ-setG ⊂X such that the intersectionG ∩U is connected for any open connectedU ⊂X. (Here Π₁, Π₁⊂X are the standard subsets of the Hilbert cubeQ absorbing for the classes of analytic and coanalytic spaces, respectively.) Similar results are obtained for higher projective classes. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 35–51, July, 1997. Translated by O. V. Sipacheva     

Sequence spaces of fuzzy real numbers defined by Orlicz functions

In this article we study different properties of convergent, null and bounded sequence spaces of fuzzy real numbers defined by an Orlicz function, like completeness, solidness, symmetricity, convergence free etc. We prove some inclusion results, too. The work of the first author was carried under University Grants Commission of India project No.-F. No. 30-240/2004 (RS).     

On completion of fuzzy metric spaces

Completions of fuzzy metric spaces (in the sense of George and Veeramani) are discussed. A complete fuzzy metric space Y is said to be a˜fuzzy metric completion of a˜given fuzzy metric space X if X is isometric to a˜dense subspace of Y. We present an example of a˜fuzzy metric space that does not admit any fuzzy metric completion. However, we prove that every standard fuzzy metric space has an (up to isometry) unique fuzzy metric completion. We also show that for each fuzzy metric space there is an (up to uniform isomorphism) unique complete fuzzy metric space that contains a˜dense subspace uniformly isomorphic to it.     

On the bilinear and cubic forms of some symplectic connected sums

Let ( M1 , M2 , N ) be three symplectic manifolds and suppose that we can do the symplectic connected sum of M1 and M2 along their submanifold N to obtain M1#NM2 . In this paper, we consider the bilinear and cubic forms of H* (M1#NM2 , Z) when dim M1#NM2 = 4, 6. Under some conditions, we get some relations of the bilinear and the cubic forms between M1#NM2 and M1■M2 .