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本文的主要目的是建立收缩核与近似连续之间的联系,基于半连续函数概念,我们构造了一类收缩核,得到了关于这一概念的许多的性质与例子,证明并解释了半收缩核与拓扑折送之间的关系。 相似文献
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在此文中我们得到如下结论:1)每个具有紧邻域扩充性质的可逼近紧空间是绝对邻域收缩核;2)每个具有紧邻域扩充性质的局部紧空间是绝对邻域收缩核。 相似文献
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本文定义了随机绝对收缩核的概念,证明了广义 Shauder 不动点定理的随机类比。同时,还证明了几个有用的引理。 相似文献
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蹇人宜 《数学年刊A辑(中文版)》1996,(4)
本文建立了具非退化半解析核的再生核空间与l_ ~2上一定算子的值域间的对应;指出了在这类空间上的紧解析乘子和拟幂零解析乘子均为零.指出了在一般情况下,这类空间不是L2(ID)的闭子空间;给出了使它们为L2(ID)的闭子空间的一个充分条件. 相似文献
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讨论了W12[a,b]能否扩大为含有有间断点函数的再生核空间的问题.结论是:若再生核空间W W12[a,b]含有有间断点的函数,则间断点必固定、间断点个数必有限且非端点a,b.进一步,我们构造了函数含有n个间断点的再生核空间并给出其再生核表达式. 相似文献
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Continua that are approximative absolute neighborhood retracts (AANR's) are characterized as absolute terminal retracts, i.e.,
retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense
arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any
of the classes of: tree-like continua, λ-dendroids, dendroids, arc-like continua and arc-like λ-dendroids is an approximative
absolute retract (so it is an AANR). Consequently, all these continua have the fixed point property, which is a new result
for absolute retracts for tree-like continua. Related questions are asked. 相似文献
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Wang Yangeng 《数学学报(英文版)》1997,13(3):333-336
The space of continuous maps from a topological spaceX to topological spaceY is denoted byC(X,Y) with the compact-open topology. In this paper we prove thatC(X,Y) is an absolute retract ifX is a locally compact separable metric space andY a convex set in a Banach space. From the above fact we know thatC(X,Y) is homomorphic to Hilbert spacel
2 ifX is a locally compact separable metric space andY a separable Banach space; in particular,C(R
n,Rm) is homomorphic to Hilbert spacel
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This research is supported by the Science Foundation of Shanxi Province's Scientific Committee 相似文献
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The paper describes some basic geometric tools to construct bilipschitz embeddings of metric spaces into (finite-dimensional) Euclidean or hyperbolic spaces. One of the main results implies the following: If X is a geodesic metric space with convex distance function and the property that geodesic segments can be extended to rays, then X admits a bilipschitz embedding into some Euclidean space iff X has the doubling property, and X admits a bilipschitz embedding into some hyperbolic space iff X is Gromov hyperbolic and doubling up to some scale. In either case the image of the embedding is shown to be a Lipschitz retract in the target space, provided X is complete. 相似文献
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L. Gó rniewicz S. A. Marano M. Slosarski 《Proceedings of the American Mathematical Society》1996,124(9):2675-2683
For a class of contractive multivalued maps defined on a complete absolute retract and with closed bounded values, the set of fixed points is proved to be an absolute retract. This result unifies and extends to arbitrary absolute retracts both Theorem 1 by Ricceri [Atti Accad. Naz. Lincei Rend. Cl.Sci. Fis. Mat. Natur. (8) 81 (1987), 283--286] and Theorem 1 by Bressan, Cellina, and Fryszkowski [Proc. Amer. Math. Soc. 112 (1991), 413--418].
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In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1. 相似文献
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Nguyen To Nhu Jose M. R. Sanjurjo Tran Van An 《Proceedings of the American Mathematical Society》1997,125(10):3075-3087
We prove that the original compact convex set with no extreme points, constructed by Roberts (1977) is an absolute retract, therefore is homeomorphic to the Hilbert cube. Our proof consists of two parts. In this first part, we give a sufficient condition for a Roberts space to be an AR. In the second part of the paper, we shall apply this to show that the example of Roberts is an AR.
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Jakob G. Simonsen 《Mathematical Logic Quarterly》2006,52(4):323-330
A metric space is said to be locally non‐compact if every neighborhood contains a sequence that is eventually bounded away from every element of the space, hence contains no accumulation point. We show within recursive mathematics that a nonvoid complete metric space is locally non‐compact iff it is without isolated points. The result has an interesting consequence in computable analysis: If a complete metric space has a computable witness that it is without isolated points, then every neighborhood contains a computable sequence that is eventually computably bounded away from every computable element of the space. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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X为自反、严格凸Banach 空间,L为X中闭子空间,P:X→L为单值算子,该文给出P成为L上度量投影P_L的判据及P_L为线性算子的充分必要条件.在自反Banach空间中,利用对偶映射,给出超平面上(值)度量投影的表达式.对于自反、严格凸、光滑的Banach 空间中线性流形上的(单值)度量投影,利用广义右逆的表示,求出其表达式.在后继文章中将给出此表达式的应用. 相似文献
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Riccardo Piergallini 《Topology and its Applications》1985,20(3):257-278
We introduce the concept of topological collapsing as a topological abstraction of polyhedral ones. Then we use this concept to characterize the cylindrical neighborhoods of a closed X in a locally compact separable metric space M such that M - X is a 3-manifold. We also prove the following criterion of existence: X has cylindrical neighborhoods in M iff there is a neighborhood N of X in M which is topologically collapsible onto X respecting Bd(M - X). 相似文献
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<正> 序言.在同倫論中,常常需要考慮滿足這種性質的拓撲空間X設Y為任意的一個正規空間,B為Y的任何一個非空閉集,任何一個由B×(0,1)+Y×(0)到X的映像都可以扩充為一個由Y×(0,1)到X的映像,我們稱這種性質為絕對同倫扩充性質,具有這種性質的空間以及用AHE表示.Borsuk曾經介紹這樣一個重要的定理: 相似文献