共查询到20条相似文献,搜索用时 15 毫秒
1.
We show that the set of semi-Lipschitz functions, defined on a quasi-metric space (X, d), that vanish at a fixed point x0X can be endowed with the structure of a quasi-normed semilinear space. This provides an appropriate setting in which to characterize both the points of best approximation and the semi-Chebyshev subsets of quasi-metric spaces. We also show that this space is bicomplete. 相似文献
2.
Let (X, d) be a quasi-metric space and (Y, q) be a quasi-normed linear space. We show that the normed cone of semi-Lipschitz functions from (X, d) to (Y, q) that vanish at a point x
0 ∈ X, is balanced. Moreover, it is complete in the sense of D. Doitchinov whenever (Y, q) is a biBanach space.
The authors acknowledge the support of Plan Nacional I+D+I and FEDER, under grant MTM2006-14925-C02-01. The second listed
author is also supported by a grant FPI from the Spanish Ministry of Education and Science. 相似文献
3.
Summary We obtain several properties of the normed cone of semi-Lipschitz functions defined on a quasi-metric space (X,d) that vanish at a fixed point x0∈X. For instance, we prove that it is both bicomplete and right K-sequentially complete, and the unit ball is compact with respect to the topology of quasi-uniform convergence. Furthermore, it has a structure of a Banach space if and only if (X,d) is a metric space. 相似文献
4.
Let X be a (metrizable) space. A mixer for X is, roughly speaking, a map μ:X3→X such that μ(x, x, y) = μ(x, y, x) = μ(y, x, x) = x for all x, y ∈ X. We show that each AR has a mixer and that a finite dimensional path connected space with a mixer is an AR. Our main result is that each separable space with a mixer and having an open cover by sets contractible within the whole space, is LEC. 相似文献
5.
Eike Hertel 《Geometriae Dedicata》1994,52(3):215-220
A subsetS of a metric space (X,d) is calledd-convex if for any pair of pointsx,y S each pointz X withd(x,z) +d(z,y) =d(x,y) belongs toS. We give some results and open questions concerning isometric and convexity-preserving embeddings of finite metric spaces into standard spaces and the number ofd-convex sets of a finite metric space. 相似文献
6.
7.
It is well known that if (X,q) is an asymmetric normed linear space, then the function qs defined on X by qs(x)=max{q(x),q(−x)}, is a norm on the linear space X. However, the lack of symmetry in the definition of the asymmetric norm q yields an algebraic asymmetry in the dual space of (X,q). This fact establishes a significant difference with the standard results on duality that hold in the case of locally convex spaces. In this paper we study some aspects of a reflexivity theory in the setting of asymmetric normed linear spaces. In particular, we obtain a version of the Goldstine Theorem to these spaces which is applied to prove, among other results, a characterization of reflexive asymmetric normed linear spaces. 相似文献
8.
The relationship between the Wijsman topology and (proximal) hit-and-miss topologies is studied in the realm of quasi-metric spaces. We establish the equivalence between these hypertopologies in terms of Urysohn families of sets. Our results generalize well-known theorems and provide easier proofs. In particular, we prove that for a quasi-pseudo-metrizable space (X,T) the Vietoris topology on the set P
0(X) of all nonempty subsets of X is the supremum of all Wijsman topologies associated with quasi-pseudo-metrics compatible with T. We also show that for a quasi-pseudo-metric space (X,d) the Hausdorff extended quasi-pseudo-metric is compatible with the Wijsman topology on P
0(X) if and only if d
–1 is hereditarily precompact. 相似文献
9.
Bessem Samet 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(12):4508-4517
Let X be a non-empty set and F:X×X→X be a given mapping. An element (x,y)∈X×X is said to be a coupled fixed point of the mapping F if F(x,y)=x and F(y,x)=y. In this paper, we consider the case when X is a complete metric space endowed with a partial order. We define generalized Meir-Keeler type functions and we prove some coupled fixed point theorems under a generalized Meir-Keeler contractive condition. Some applications of our obtained results are given. The presented theorems extend and complement the recent fixed point theorems due to Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393]. 相似文献
10.
Michel Las Vergnas 《Discrete Mathematics》1976,15(1):27-39
The main result of this paper is the following theorem: Let G = (X,E) be a digraph without loops or multiple edges, |X| ?3, and h be an integer ?1, if G contains a spanning arborescence and if d+G(x)+d?G(x)+d?G(y)+d?G(y)? 2|X |?2h?1 for all x, y?X, x ≠ y, non adjacent in G, then G contains a spanning arborescence with ?h terminal vertices. A strengthening of Gallai-Milgram's theorem is also proved. 相似文献
11.
Michael Hrušák Tamás Mátrai Aleš Nekvinda Václav Vlasák Ondřej Zindulka 《Acta Mathematica Hungarica》2014,142(1):1-30
A metric space (X,d) is monotone if there is a linear order < on X and a constant c>0 such that d(x,y)≦cd(x,z) for all x<y<z∈X. Properties of continuous functions with monotone graph (considered as a planar set) are investigated. It is shown, for example, that such a function can be almost nowhere differentiable, but must be differentiable at a dense set, and that the Hausdorff dimension of the graph of such a function is 1. 相似文献
12.
A. Jiménez-Vargas A. Morales Campoy 《Journal of Mathematical Analysis and Applications》2010,366(1):195-201
We show that the isometry groups of Lip(X,d) and lip(X,dα) with α∈(0,1), for a compact metric space (X,d), are algebraically reflexive. We also prove that the sets of isometric reflections and generalized bi-circular projections on such spaces are algebraically reflexive. In order to achieve this, we characterize generalized bi-circular projections on these spaces. 相似文献
13.
We construct a functor AC(?, ?) from the category of path connected spaces X with a base point x to the category of simply connected spaces. The following are the main results of the paper: (i) If X is a Peano continuum then AC(X, x) is a cell-like Peano continuum; (ii) If X is n-dimensional then AC(X, x) is (n + 1)?dimensional; and (iii) For a path connected space X, π 1(X, x) is trivial if and only if π 2(AC(X, x)) is trivial. As a corollary, AC(S 1, x) is a 2-dimensional nonaspherical cell-like Peano continuum. 相似文献
14.
《Quaestiones Mathematicae》2013,36(3):359-374
For any weightable quasi-metric space (X, d) having a maximum with respect to the associated order ≤ d , the notion of the quasi-metric of complexity convergence on the the function space (equivalently, the space of sequences) Xω , is introduced and studied. We observe that its induced quasi-uniformity is finer than the quasi-uniformity of pointwise convergence and weaker than the quasi-uniformity of uniform convergence. We show that it coincides with the quasi-uniformity of pointwise convergence if and only if the quasi-metric space (X, d) is bounded and it coincides with the quasi-uniformity of uniform convergence if and only if X is a singleton. We also investigate completeness of the quasi-metric of complexity convergence. Finally, we obtain versions of the celebrated Grothendieck theorem in this context. 相似文献
15.
Alan P Sprague 《Journal of Combinatorial Theory, Series B》1978,24(3):294-300
We denote the distance between vertices x and y of a graph by d(x, y), and pij(x, y) = ∥ {z : d(x, z) = i, d(y, z) = j} ∥. The (s, q, d)-projective graph is the graph having the s-dimensional subspaces of a d-dimensional vector space over GF(q) as vertex set, and two vertices x, y adjacent iff . These graphs are regular graphs. Also, there exist integers λ and μ > 4 so that μ is a perfect square, p11(x, y) = λ whenever d(x, y) = 1, and p11(x, y) = μ whenever d(x, y) = 2. The (s, q, d)-projective graphs where and , are characterized by the above conditions together with the property that there exists an integer r satisfying certain inequalities. 相似文献
16.
Jian YuDingtao Peng Shuwen Xiang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6326-6332
Let X be a nonempty, convex and compact subset of normed linear space E (respectively, let X be a nonempty, bounded, closed and convex subset of Banach space E and A be a nonempty, convex and compact subset of X) and f:X×X→R be a given function, the uniqueness of equilibrium point for equilibrium problem which is to find x∗∈X (respectively, x∗∈A) such that f(x∗,y)≥0 for all y∈X (respectively, f(x∗,y)≥0 for all y∈A) is studied with varying f (respectively, with both varying f and varying A). The results show that most of equilibrium problems (in the sense of Baire category) have unique equilibrium point. 相似文献
17.
We study the hyperspace K
0(X) of non-empty compact subsets of a Smyth-complete quasi-metric space (X, d). We show that K
0(X), equipped with the Hausdorff quasi-pseudometric H
d
forms a (sequentially) Yoneda-complete space. Moreover, if d is a T
1 quasi-metric, then the hyperspace is algebraic, and the set of all finite subsets forms a base for it. Finally, we prove
that K
0(X), H
d
) is Smyth-complete if (X, d) is Smyth-complete and all compact subsets of X are d
−1-precompact. 相似文献
18.
T Cacoullos 《Statistics & probability letters》1983,1(5):269-272
Given that the conditional distribution ps(y|x) of Y, given X = x is an x-fold convolution of a nonnegative integer-valued r.v. ξ for every s= P[ξ = 0] > 0, the distribution of X, hence also of Y, is characterized by the regression point m(0) = E[X|Y = 0]. An infinite variety of generalized distributions (of Y) can be characterized by arbitrarily varying the distribution of X. 相似文献
19.
For every metric space (X, d) and origin o ∈ X, we show the inequality I o (x, y) ≤ 2d o (x, y), where I o (x, y) = d(x, y)/d(x, o)d(y, o) is the metric space inversion semimetric, d o is a metric subordinate to I o , and x, y ∈ X \ {o} The constant 2 is best possible. 相似文献
20.
It was proved by R. Gomory and T. Hu in 1961 that, for every finite nonempty ultrametric space (X, d), the inequaliy \( \left| {\mathrm{Sp}(X)} \right|\leq \left| X \right|-1 \), where Sp(X) = {d(x, y) : x, y ∈ X, x ≠ y} , holds. We characterize the spaces X for which the equality is attained by the structural properties of some graphs and show that the set of isometric types of such X is dense in the Gromov–Hausdorff space of the isometric types of compact ultrametric spaces. 相似文献