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1.
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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Li has introduced the concepts of inverse system and direct system for fuzzy topological spaces and studied inverse limits and direct limits on such spaces by presenting the explicit constructions of these limits.In this paper some important concepts of fuzzy topology,such as,product fuzzy topology,quotient fuzzy topology,fuzzy continuity etc.,are used for further study of inverse limits and direct limits for fuzzy topological spaces. 相似文献
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正规可遮空间的逆极限 总被引:17,自引:0,他引:17
本文得到如下结果:设X是逆系统{Xα,π^αβ,A}的极限,│Λ│=λ,假设每个投射πα:X→Xα是开且到上的,X是λ-仿紧的,如果每个Xα是正规可遮的,则X是仿紧的。进一步得到了关于遗传正规且遗传可遮的类似结果。 相似文献
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得到了如下结果:设X是逆系统{Xα,παβ,Λ}的逆极限,|Λ|=λ,假设每个映射πα∶X→Xα是开的且到上的,X是λ-仿紧,每个Xα是正规可数仿紧的,则X是正规可数仿紧的.进一步得到了关于遗传正规且遗传可数仿紧空间的类似结果. 相似文献
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This paper proves the following results: Let X = lim← { Xσ,π^σρ,∧ },| ∧ | =λ, and every pro-jection πσ : X → Xσ be an open and onto mapping. (A) If X is λ-paracompact and every Xσ is normal and δθ-refinable, then X is normal and δθ-refinable; (B) If X is hereditarily λ-pamcompact and every Xσ is hereditarily normal and hereditarily δθ-refinable, then X is hereditarily normal and hereditarily δθ-refiable. 相似文献
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The main question discussed in this paper is how well a finite metric space of size n can be embedded into a graph with certain topological restrictions.
The existing constructions of graph spanners imply that any n -point metric space can be represented by a (weighted) graph with n vertices and n
1 +O(1/r)
edges, with distances distorted by at most r . We show that this tradeoff between the number of edges and the distortion cannot be improved, and that it holds in a much
more general setting. The main technical lemma claims that the metric space induced by an unweighted graph H of girth g cannot be embedded in a graph G (even if it is weighted) of smaller Euler characteristic, with distortion less than g/4 - 3/2 . In the special case when |V(G)| =|V(H)| and G has strictly less edges than H , an improved bound of g/3 - 1 is shown. In addition, we discuss the case χ(G) < χ(H) - 1 , as well as some interesting higher-dimensional analogues. The proofs employ basic techniques of algebraic topology.
Received September 26, 1995, and in revised form March 18, 1996. 相似文献
7.
We investigate the metric generalized inverses of linear operators in Banach spaces and their homogeneous selections, which
was the research suggestion given by Nashed and Votruba (Bull. Am. Math. Soc. 80:831–835, 1974). We construct a kind of the bounded homoneneous selections for the set-valued metric generalized inverse. Criteria for the
metric generalized inverses of linear operators and their homogeneous selections are given in terms of Moore–Penrose conditions.
The research was supported in part by the National Science Foundation Grant (10671049) and the Science Foundation Grant of
Heilongjiang Province. 相似文献
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Given a metric space with a Borel measure , we consider a class of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function p-summable with respect to . We prove some analogs of the classical theorems on embedding Sobolev function classes into Lebesgue spaces. 相似文献
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Violeta Leoreanu 《Southeast Asian Bulletin of Mathematics》2002,25(3):421-426
In this paper, it is proved that the direct limit (inverse limit) of an SHR direct (respectively, inverse) family of SHR semigroups is an SHR semigroup.AMS Subject Classifications Primary 20N20 Secondary 20M99 相似文献
14.
本文用度量空间的mssc-映象给出了N-空间一些刻画,证明了空间X是N-空间当且仅当X是度量空间的序列覆盖(序列商)mssc-映象,肯定地回答了关于N-空间的一个猜想。 相似文献
15.
Magnitude is a numerical invariant of metric spaces introduced by Leinster, motivated by considerations from category theory. This paper extends the original definition for finite spaces to compact spaces, in an equivalent but more natural and direct manner than in previous works by Leinster, Willerton, and the author. The new definition uncovers a previously unknown relationship between magnitude and capacities of sets. Exploiting this relationship, it is shown that for a compact subset of Euclidean space, the magnitude dimension considered by Leinster and Willerton is equal to the Minkowski dimension. 相似文献
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A Metric on Probabilities, and Products of Loeb Spaces 总被引:1,自引:0,他引:1
Two functions on finitely additive probability spaces that behavewell under products are introduced: discrepancy, which measureshow close one space comes to extending another, and bi-discrepancy,which is a pseudo-metric on the collection of all spaces ona given set, and a metric on the collection of complete spaces.These are then applied to show that the Loeb space of the internalproduct of two internal finitely additive probability spacesdepends only on the Loeb spaces of the two original internalspaces. Thus the notion of a Loeb product of two Loeb spacesis well defined. The Loeb operation induces an isometry fromthe nonstandard hull of the space of internal probability spaceson a given set to the space of Loeb spaces on that set, withthe metric of bi-discrepancy. 相似文献
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J. J. Grobler 《Integral Equations and Operator Theory》2007,57(1):83-99
For a probability space
we denote the marginal measures of
, defined on Σ and Λ respectively, by
and
. If ρ is a function norm defined on
marginal function norms ρ1 and ρ2 are defined on
and
. We find conditions which guarantee Lρ 1 + Lρ 2 to be embedded in Lρ as a closed subspace. The problem is encountered in Statistics when estimating a bivariate distribution with known marginals.
We find a condition which, applied to the binormal distribution in L2, improves some known conditions. 相似文献
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Potential Analysis - In the setting of a complete metric space that is equipped with a doubling measure and supports a Poincaré inequality, we show that the total variation of functions of... 相似文献