共查询到20条相似文献,搜索用时 750 毫秒
1.
Charles B. Dunham 《Aequationes Mathematicae》1995,49(1):295-299
Summary LetF be an approximating function with parameter setP, a subset ofn-space, on an intervalI satisfying the hypotheses of Meinardus and Schwedt (the local Haar condition and propertyZ) which result in an alternating theory. Consider uniform approximation to functionf onX, a finite subset ofI. A sufficient condition is given, involving best parameters being in a closed set, on which the degree isn that a family of functionsf have a uniform (parameterwise) local strong uniqueness constant > 0. The necessity of the condition in this and related problems, in particular ordinary rational approximation on an interval, is examined. 相似文献
2.
It is possible to consider two variants of cluster theory: Inaffine cluster theory, one considers collections ofsubsets of a given setX of objects or states, whereas inprojective cluster theory, one considers collections ofsplits (orbipartitions) of that set. In both contexts, it can be desirable to produce acontinuous model, that is, a spaceT encompassing the given setX which represents in a well-specified and more or less parsimonious way all possibleintermediate objects ortransition states compatible with certain restrictions derived from the given collection of subsets or splits. We investigate an interesting and intriguing relationship between two such constructions that appear in the context of projective cluster theory: TheBuneman construction and thetight-span (or justT)construction. 相似文献
3.
Paulette Saab 《Aequationes Mathematicae》1980,20(1):252-262
LetX be any compact convex subset of a locally convex Hausdorff space andE be a complex Banach space. We denote byA(X, E) the space of all continuous and affineE-valued functions defined onX. In this paper we prove thatX is a Choquet simplex if and only if the dual ofA(X, E) is isometrically isomorphic by a selection map toM
m
(X, E*), the space ofE*-valued,w*-regular boundary measures onX. This extends and strengthens a result of G. M. Ustinov. To do this we show that for any compact convex setX, each element of the dual ofA(X, E) can be represented by a measure inM
m
(X, E*) with the same norm, and this representation is unique if and only ifX is a Choquet simplex. We also prove that ifX is metrizable andE is separable then there exists a selection map from the unit ball of the dual ofA(X, E) into the unit ball ofM
m
(X, E*) which is weak* to weak*-Borel measurable.This work will constitute a portion of the author's Ph.D. Thesis at the University of Illinois. 相似文献
4.
G. F. Clements 《Periodica Mathematica Hungarica》1992,25(2):119-126
IfX is a family ofl-subsets of a multiset, then there is a set of distinct representatives of the members ofX among the (l-k)-subsets of the members ofX provided the cardinality ofX does not exceed a certain bound. An algorithm for calculating this bound is given. 相似文献
5.
Zhao Xuezhi 《数学学报(英文版)》1996,12(1):71-76
Letf:XX be a selfmap of a compact connected polyhedron, andA a nonempty closed subset ofX. In this paper, we shall deal with the question whether or not there is a mapg:XX homotopic tof such that the fixed point set Fixg ofg equalsA. We introduce a necessary condition for the existence of such a mapg. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.Partially supported by the Natural Science Foundation of Liaoning University. 相似文献
6.
Bin He 《Mathematical Logic Quarterly》2005,51(5):462-469
We prove a partition theorem for analytic sets, namely, if X is an analytic set in a Polish space and [X]n = K0 ∪ K1 with K0 open in the relative topology, and the partition satisfies a finitary condition, then either there is a perfect K0‐homogeneous subset or X is a countable union of K1‐homogeneous subsets. We also prove a partition theorem for analytic sets in the three‐dimensional case. Finally, we give some applications of the theorems. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
N. Hadjisavvas D. Kravvaritis I. Polyrakis 《Rendiconti del Circolo Matematico di Palermo》1994,43(1):119-126
In this paper we study the weakly compact subset ofL
1(μ,X) and bvca(Σ,X), supposing that proper subsets ofX andX
* have the Radom-Nikodym property. 相似文献
8.
V.S. Balaganskii 《Journal of Approximation Theory》1997,89(3):372-379
In this work we study a relative Chebyshev center ofKwith respect toY, whereKis a closed bounded convex subset of a Hilbert spaceX, andYis a closed convex subset ofX. Some results of Amir and Mach [J. Approx. Theory40, (1984), 364–374] are extended. 相似文献
9.
10.
Libor Veselý 《Archiv der Mathematik》2002,79(6):499-506
Given a Banach spaceX, letc
0(X) be the space of all null sequences inX (equipped with the supremum norm). We show that: 1) each compact set inc
0(X) admits a (Chebyshev) center iff each compact set inX admits a center; 2) forX satisfying a certain condition (Q), each bounded set inc
0(X) admits a center iffX is quasi uniformly rotund. We construct a Banach spaceX such that the compact subsets ofX admit centers,X satisfies the condition (Q) andX is not quasi uniformly rotund. It follows that the Banach spaceE=c
0(X) has the property from the title.
Eine überarbeitete Fassung ging am 4. 7. 2001 ein 相似文献
11.
N. V. Zhivkov 《Set-Valued Analysis》1995,3(2):195-209
For every uniformly convex Banach spaceX with dimX2 there is a residual setU in the Hausdorff metric spaceB(X) of bounded and closed sets inX such that the metric projection generated by a set fromU is two-valued and upper semicontinuous on a dense and everywhere continual subset ofX. For any two closed and separated subsetsM
1 andM
2 ofX the points on the equidistant hypersurface which have best approximations both inM
1 andM
2 form a dense G set in the induced topology.The author is partially supported by the National Fund for Scientific Research at the Bulgarian Ministry of Science and Education under contract MM 408/94. 相似文献
12.
We prove that ifX is a Polish space andF a face ofP(X) with the Baire property, thenF is either a meager or a co-meager subset ofP(X). As a consequence we show that for every abelian Polish groupX and every analytic Haar-null set Λ⊆X, the set of test measuresT(Λ) of Λ is either meager or co-meager. We characterize the non-locally-compact groups as the ones for which there exists
a closed Haar-null setF⊆X withT(F) meager, Moreover, we answer negatively a question of J. Mycielski by showing that for every non-locally-compact abelian Polish
group and every σ-compact subgroupG ofX there exists aG-invariantF
σ subset ofX which is neither prevalent nor Haar-null.
Research supported by a grant of EPEAEK program “Pythagoras”. 相似文献
13.
We give a functional Korovkin-type theorem onB(X), the space of bounded complex-valued functions on an arbitrary setXand investigate a BKW-operator onB(X) for a finite collection of test functions with a suitable property and a seminorm defined by a finite subset ofX. 相似文献
14.
Gun-Marie Lövblom 《Israel Journal of Mathematics》1986,56(2):143-159
We characterize the isometries fromC(X) intoC(Y) whereX andY are compact metric spaces. We give necessary and sufficient conditions on an isometry from a subset ofC(X) intoC(Y) to have an extension to the whole space. It is also shown that an almost isometry from the unit ball ofC(X) into the unit ball ofC(Y) is near to an isometry. 相似文献
15.
It is well-known that ifX is a compact metric space and ifI is a capacity onX then every analytic subset ofX isI-capacitable [2], [1]. We introduce the notion of vector-valued capacity in the case when the codomain is a Banach lattice
and we prove an analogous theorem for analytic subsets of a Polish space. Finally, we show that every vectorvalued outer measure
is a capacity and, in connection with the so-called “marginal problem”, we give an example of a capacity taking values in
a reflexive Banach lattice. 相似文献
16.
Janusz J. Charatonik 《Rendiconti del Circolo Matematico di Palermo》1995,44(3):457-468
Homeomorphisms of some special universal dendrites are considered in the paper. In particular, dendrites are characterized
for which the action onX of the group of autohomeomorphisms ofX has exactlyn≥3 orbits, and for each orbitB ofX and for each areA ⊂X the intersectionA∪B is a dense subset ofA. Some of the results generalize earlier ones from the author’s paper [2]. 相似文献
17.
The Hamming distance between two permutations of a finite setX is the number of elements ofX on which they differ. In the first part of this paper, we consider bounds for the cardinality of a subset (or subgroup) of a permutation groupP onX with prescribed distances between its elements. In the second part. We consider similar results for sets ofs-tuples of permutations; the role of Hamming distance is played by the number of elements ofX on which, for somei, the ith permutations of the two tuples differ. 相似文献
18.
Valeria Marraffa 《Journal of Theoretical Probability》1988,1(3):255-261
It is shown here that for any Banach spaceE-valued amart (X
n) of classB, almost sure convergence off(Xn) tof(X) for eachf in a total subset ofE
* implies scalar convergence toX. 相似文献
19.
Denote by the family of all real valued functions on a metric space which satisfy a Lipschitz condition on the compact (bounded) subsets of X. We prove that every homomorphism on is the evaluation at some point of X if and only if X is realcompact (every closed bounded subset of X is compact).
(Received 4 November 1998; in revised form 31 May 1999) 相似文献
20.
In every Hausdorff locally convex space for which there exists a
strictly finer topology than its weak topology but with the same bounded
sets (like for instance, all infinite dimensional Banach spaces, the
space of distributions
or the space of analytic
functions
in an open set
, etc.)
there is a set A such that 0 is in the weak closure of
A but 0
is not in the weak closure of any bounded subset B
of A. A consequence of this is that a Banach
space X is finite dimensional if,
and only if, the following property [P] holds: for each set
and each x in the weak closure of
A there is a bounded set
such that x belongs to the weak closure of
B. More generally, a
complete locally convex space X satisfies property
[P] if, and only if, either X is finite dimensional
or linearly topologically isomorphic to
.
Received: 11 June 2003 相似文献