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1.
1.σ-空间与Σ-空间 §1 积空间的仿紧性 广义度量空间理论来源于三个方面:度量化问题、积空间的仿紧性问题以及通过映象研究各类空间,这里就第二方面谈一些。 自从1944年J.Dieudonné[16]定义仿紧性以后,对仿紧性理论的研究蓬勃开展,主要是由于它包含两大类空间(度量空间与紧空间),应用广泛。但也有它的弱点:两个仿紧空间 相似文献
2.
建立非紧FC-度量空间中转移紧开值映射的Browder型不动点定理.作为应用,获得非紧FC-度量空间中一般拟平衡问题系统的平衡存在定理. 相似文献
3.
讨论了F紧性在不同值域格值拓扑空间中的乘积问题.证明了模糊子集的重积是F紧子集当且仅当每个模糊子集是F紧子集.从而,在重积空间中,F紧性的Tychonoff乘积定理成立. 相似文献
4.
非紧超凸度量空间中的一个新的极大元定理及其对抽象经济的应用(英文) 总被引:4,自引:0,他引:4
在非紧超凸度量空间中建立了一个新的极大元定理.作为应用,获得了连续选择及其不动点定理和一个Browder-Fan不动点定理.最后,新建了非紧超凸度量空间中的定性对策和抽象经济的平衡点存在定理. 相似文献
5.
非紧超凸度量空间中的一个新的极大元定理及其对抽象经济的应用 总被引:2,自引:0,他引:2
在非紧超凸度量空间中建立了一个新的极大元定理.作为应用,获得了连续选择及其不动点定理和一个Browder-Fan不动点定理.最后,新建了非紧超凸度量空间中的定性对策和抽象经济的平衡点存在定理. 相似文献
6.
非紧L-凸度量空间中的一般拟平衡问题组(英文) 总被引:1,自引:0,他引:1
本文建立了非紧完备L-凸度量空间中新的不动点定理.作为应用,获得了非紧完备L-凸度量空间中的一般拟平衡问题组和拟平衡问题组的平衡存在定理. 相似文献
8.
文开庭 《应用泛函分析学报》2010,12(3):266-273
引入了FC-度量空间,建立了非紧FC-度量空间中的R-KKM定理.作为应用,研究了非紧FC-度量空间中的变分不等式的解集、相交点集、Ky Fan截口和极大元集的性质,获得了FC-度量空间中的Fan-Browder不动点定理. 相似文献
9.
本文引入GFC-度量空间,建立GFC-度量空间中GR-KKM定理.作为应用,在非紧框架下,得到GFC-度量空间的相交点集、Ky Fan截口和极大元集为非空紧集. 相似文献
10.
本文给出了广义H-空间的完备性特征性质和紧性特征性质,同时也研究了这一空间的度量化定理.作为这些理论的应用.我们得到了Menger概率度量空间的完备性特征和紧性特征.给出了该空间的度量化函数的具体形式. 相似文献
11.
R.A. McCoy 《Topology and its Applications》2010,157(16):2516-2537
A study is made of two classes of product topologies on powers of spaces: the general box product topologies, and the general uniform product topologies. Some examples are given and some results are shown about the properties of these general product spaces. This is applied to show that certain spaces of continuous functions with the fine topology are homeomorphic to box product spaces, and certain spaces of continuous functions with the uniform topology are homeomorphic to uniform product spaces. 相似文献
12.
Arnold W. Miller 《Topology and its Applications》1982,14(3):313-317
We prove two theorems about box products. The first theorem says that the box product of countable spaces is pseudonormal, i.e. any two disjoint closed sets one of which is countable can be separated by open sets. The second theorem says that assuming CH a certain uncountable box product is normal (i.e. <ω1?□α<ω1Xα where each Xα is a compact metric space). 相似文献
13.
J. E. Vaughan 《Indagationes Mathematicae》2001,12(4):585
It is well known that spaces defined from a separated uniform structure with a linearly ordered base of uncountable cofinality (ωμ-metrizable spaces) are ultraparacompact and have an ortho-base, hence are non-Archimedean spaces in the sense of A. Monna. Our results concern whether certain wider classes of spaces defined from linear structures retain these properties. We construct for every regular cardinal ωμ, examples of ωμ-additive, ωμ-stratifiable spaces (i.e., ωμ-Nagata spaces) that do not have an ortho-base. We give a number of examples of linearly stratifiable spaces, one of which is related to an example of Eric K. van Douwen concerning countable box products of stratifiable spaces. 相似文献
14.
A. Khukhro 《Journal of Functional Analysis》2012,263(1):115-128
We investigate how coarse embeddability of box spaces into Hilbert space behaves under group extensions. In particular, we prove a result which implies that a semidirect product of a finitely generated free group by a finitely generated residually finite amenable group has a box space which coarsely embeds into Hilbert space. This provides a new class of examples of metric spaces with bounded geometry which coarsely embed into Hilbert space but do not have property A, generalising the example of Arzhantseva, Guentner and Spakula. 相似文献
15.
M. J. Johnson 《Constructive Approximation》1997,13(2):155-176
An upper bound on theL
p-approximation power (1 ≤p ≤ ∞) provided by principal shift-invariant spaces is derived with only very mild assumptions on the generator. It applies
to both stationary and nonstationary ladders, and is shown to apply to spaces generated by (exponential) box splines, polyharmonic
splines, multiquadrics, and Gauss kernel. 相似文献
16.
Yi Huang 《Archiv der Mathematik》2018,111(6):633-646
In this article we generalize the singular integral operator theory on weighted tent spaces to spaces of homogeneous type. This generalization of operator theory is in the spirit of C. Fefferman and Stein since we use some auxiliary functionals on tent spaces which play roles similar to the Fefferman–Stein sharp and box maximal functions in the Lebesgue space setting. Our contribution in this operator theory is twofold: for singular integral operators (including maximal regularity operators) on tent spaces pointwise Carleson type estimates are proved and this recovers known results; on the underlying space no extra geometrical conditions are needed and this could be useful for future applications to parabolic problems in rough settings. 相似文献
17.
A. A. Ivanov 《Journal of Mathematical Sciences》2000,98(5):617-623
The purpose of the paper is to extend the notions of splitting and jointly continuous topologies on function spaces to products
of spaces, to present a new theory of duality between topologies on function spaces and topologies on products of spaces,
and to generalize these theories to bitopological spaces. The author starts from the definitions well known in the literature.
Bibliography: 1 title.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 242, 1997, pp. 217–229.
Translated by N. Yu. Netsvetaev. 相似文献
18.
Secondary homotopy operations called box bracket operations were defined in the homotopy theory of an arbitrary 2-category
with zeros by Hardie, Marcum and Oda (Rend Ist Mat Univ Trieste, 33:19–70 2001). For the topological 2-category of based spaces, based maps and based track classes of based homotopies, the classical Toda
bracket is a particular example of a box bracket operation and subsequent development of the theory has refined, clarified
and placed in this more general context many of the properties of classical Toda brackets. In this paper, and for the topological
case only, we use an inductive definition to extend the theory to long box brackets. As is well-known, the necessity to manage
higher homotopy coherence is a complicating factor in the consideration of such higher order operations. The key to our construction
is the definition of an appropriate triple box bracket operation and consequently we focus primarily on the properties of
the triple box bracket. We exhibit and exploit the relationship of the classical quaternary Toda bracket to the triple box
bracket. As our main results we establish some computational techniques for triple box brackets that are based on composition
methods. Some specific computations from the homotopy groups of spheres are included. 相似文献
19.
Joël Rouyer 《Topology and its Applications》2011,158(16):2140-2147
We prove that there is a residual subset of the Gromov-Hausdorff space (i.e. the space of all compact metric spaces up to isometry endowed with the Gromov-Hausdorff distance) whose elements enjoy several unexpected properties. In particular, they have zero lower box dimension and infinite upper box dimension. 相似文献
20.
Foundations of Computational Mathematics - This paper analyzes the approximation properties of spaces of piecewise tensor product polynomials over box meshes with a focus on application to... 相似文献