共查询到20条相似文献,搜索用时 0 毫秒
1.
本文采用Kalava和Seikkala的模糊度量空间定义,利用文(7)中建立的亚度量簇生成空间理论,研究了Fuzzy度量空间中的单值映射的Caristi型不动点定理以及它在Menger概率度量空间中的应用。 相似文献
2.
Oleksiy Dovgoshey Dmytro Dordovskyi 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(2):100-113
The paper deals with pretangent spaces to general metric spaces. An ultrametricity criterion for pretangent spaces is found
and it is closely related to the metric betweenness in the pretangent spaces. 相似文献
3.
A. A. Ivanov 《Journal of Mathematical Sciences》2008,153(1):38-42
The paper contains some initial results of the theory of weakly metric spaces. The weak triangle axiom: for any ε > 0 there
exists δ > 0 such that for any points x, y, and z with d(y, z) ≤ δ, the inequality d(x, z) ≤ d(x, y) + ε holds.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 352, 2008, pp. 94–105. 相似文献
4.
Gerald Kuba 《Archiv der Mathematik》2011,97(6):569-578
If κ is a cardinal number, then any class of mutually non-homeomorphic metric spaces of size κ must be a set whose cardinality cannot exceed 2
κ
. Our main result is a vivid construction of 2
κ
mutually non-homeomorphic complete and both path connected and locally path connected metric spaces of size κ for each cardinal number κ from continuum up. Additionally we also deal with counting problems concerning countable metric spaces and Euclidean spaces. 相似文献
5.
6.
Let
Md{\cal M}^d
be an arbitrary real normed space of finite dimension d ≥ 2. We define the metric capacity of
Md{\cal M}^d
as the maximal
m ? \Bbb Nm \in {\Bbb N}
such that every m-point metric space is isometric to some subset of
Md{\cal M}^d
(with metric induced by
Md{\cal M}^d
). We obtain that the metric capacity of
Md{\cal M}^d
lies in the range from 3 to
ë\frac32d
û+1\left\lfloor\frac{3}{2}d\right\rfloor+1
, where the lower bound is sharp for all d, and the upper bound is shown to be sharp for d ∈ {2, 3}. Thus, the unknown sharp upper bound is asymptotically linear, since it lies in the range from d + 2 to
ë\frac32d
û+1\left\lfloor\frac{3}{2}d\right\rfloor+1
. 相似文献
7.
V. V. Bilet 《Ukrainian Mathematical Journal》2013,64(9):1448-1456
8.
Let
be an arbitrary real normed space of finite dimension d ≥ 2. We define the metric capacity of
as the maximal
such that every m-point metric space is isometric to some subset of
(with metric induced by
). We obtain that the metric capacity of
lies in the range from 3 to
, where the lower bound is sharp for all d, and the upper bound is shown to be sharp for d ∈ {2, 3}. Thus, the unknown sharp upper bound is asymptotically linear, since it lies in the range from d + 2 to
.
Research supported by the German Research Foundation, Project AV 85/1-1. 相似文献
9.
Stephen H. Hechler 《Israel Journal of Mathematics》1973,14(2):115-148
For every uncountable cardinal κ define a metric spaceS to be κ-superuniversal iff for every metric spaceU of cardinality κ, every partial isometry intoS from a subset ofU of cardinality less than κ can be extended to all ofU. We prove that any such space must have cardinality at least
, and for each regular uncountable cardinal κ, we construct a κ-superuniversal metric space of cardinality
, It is proved that there is a unique κ-superuniversal metric space of cardinality κ iff
. Several decomposition theorems are also proved, e.g., every κ-superuniversal space contains a family of
disjoint κ-superuniversal subspaces. Finally, we consider some applications to more general topological spaces, to graph
theory, and to category theory, and we conclude with a list of open problems. 相似文献
10.
On fuzzy metric spaces 总被引:1,自引:0,他引:1
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. 相似文献
11.
Casey Kelleher 《Topology and its Applications》2012,159(3):749-755
Enflo (1969) [4] constructed a countable metric space that may not be uniformly embedded into any metric space of positive generalized roundness. Dranishnikov, Gong, Lafforgue and Yu (2002) [3] modified Enflo?s example to construct a locally finite metric space that may not be coarsely embedded into any Hilbert space. In this paper we meld these two examples into one simpler construction. The outcome is a locally finite metric space (Z,ζ) which is strongly non-embeddable in the sense that it may not be embedded uniformly or coarsely into any metric space of non-zero generalized roundness. Moreover, we show that both types of embedding may be obstructed by a common recursive principle. It follows from our construction that any metric space which is Lipschitz universal for all locally finite metric spaces may not be embedded uniformly or coarsely into any metric space of non-zero generalized roundness. Our construction is then adapted to show that the group Zω=ℵ0⊕Z admits a Cayley graph which may not be coarsely embedded into any metric space of non-zero generalized roundness. Finally, for each p?0 and each locally finite metric space (Z,d), we prove the existence of a Lipschitz injection f:Z→?p. 相似文献
12.
13.
We discuss the potential theory related to the variational capacity and the Sobolev capacity on metric measure spaces. We prove our results in the axiomatic framework of [17].46E35, 31C15, 31C45 相似文献
14.
Following the definition of domination of a topological space X by a metric space M introduced by Cascales, Orihuela and Tkachuk (2011) in [3], we define a topological cardinal invariant called the metric domination index of a topological space X as minimum of the set {w(M):M is a metric space that dominates X}. This invariant quantifies or measures the concept of M-domination of Cascales et al. (2011) [3]. We prove (in ZFC) that if K is a compact space such that Cp(K) is strongly dominated by a second countable space then K is countable. This answers a question by the authors of Cascales et al. (2011) [3]. 相似文献
15.
J. Chaber 《Topology and its Applications》1982,14(1):31-41
We give characterizations of perfect images and open and compact images of spaces that can be mapped onto metrizable spaces by a mapping with fibers having a given property . We use these characterizations to obtain conditions which imply that such images can be mapped onto a metric space by a mapping with fibers satisfying . Such a treatment includes the investigation of spaces with a weaker metric topology [2, Ch. 5]. 相似文献
16.
In this paper we examine the properties of EC-plastic metric spaces, spaces which have the property that any noncontractive bijection from the space onto itself must be an isometry. 相似文献
17.
Convexities of metric spaces 总被引:2,自引:0,他引:2
Shin-ichi Ohta 《Geometriae Dedicata》2007,125(1):225-250
We introduce two kinds of the notion of convexity of a metric space, called k-convexity and L-convexity, as generalizations of the CAT(0)-property and of the nonpositively curved property in the sense of Busemann, respectively.
2-uniformly convex Banach spaces as well as CAT(1)-spaces with small diameters satisfy both these convexities. Among several
geometric and analytic results, we prove the solvability of the Dirichlet problem for maps into a wide class of metric spaces.
相似文献
18.
Currents in metric spaces 总被引:8,自引:0,他引:8
19.
Intuitionistic fuzzy metric spaces 总被引:8,自引:0,他引:8
Using the idea of intuitionistic fuzzy set due to Atanassov [Intuitionistic fuzzy sets. in: V. Sgurev (Ed.), VII ITKR's Session, Sofia June, 1983; Fuzzy Sets Syst. 20 (1986) 87], we define the notion of intuitionistic fuzzy metric spaces as a natural generalization of fuzzy metric spaces due to George and Veeramani [Fuzzy Sets Syst. 64 (1994) 395] and prove some known results of metric spaces including Baire's theorem and the Uniform limit theorem for intuitionistic fuzzy metric spaces. 相似文献
20.