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1.
We show that separable, locally compact spaces with property (a) necessarily have countable extent — i.e., have no uncountable
closed, discrete subspaces — if the effective weak diamond principle ⋄(ω,ω,<) holds. If the stronger, non-effective, diamond principle Φ(ω,ω,<) holds then separable, countably paracompact spaces also have countable extent. We also give a short proof that the latter
principle implies there are no small dominating families in
ω
1
ω. 相似文献
2.
We study final group topologies and their relations to compactness properties. In particular, we are interested in situations
where a colimit or direct limit is locally compact, a k
ω-space, or locally k
ω. As a first application, we show that unitary forms of complex Kac-Moody groups can be described as the colimit of an amalgam
of subgroups (in the category of Hausdorff topological groups, and the category of k
ω-groups). Our second application concerns Pontryagin duality theory for the classes of almost metrizable topological abelian
groups, resp., locally k
ω topological abelian groups, which are dual to each other. In particular, we explore the relations between countable projective
limits of almost metrizable abelian groups and countable direct limits of locally k
ω abelian groups. 相似文献
3.
M. Rudelson 《Israel Journal of Mathematics》1995,89(1-3):189-204
We prove a variant of a theorem of N. Alon and V. D. Milman. Using it we construct for everyn-dimensional Banach spacesX andY a measure space Ω and two operator-valued functionsT: Ω→L(X, Y),S: Ω→L(Y, X) so that ∫Ω
S(ω)oT(ω)dω is the identity operator inX and ∫Ω||S(ω)||·||T(ω)||dω=O(n
α
) for some absolute constantα<1.
We prove also that any subset of the unitn-cube which is convex, symmetric with respect to the origin and has a sufficiently large volume possesses a section of big
dimension isomorphic to ak-cube.
Research supported in part by a grant of the Israel Academy of Sciences. 相似文献
4.
Eugene Wesley 《Israel Journal of Mathematics》1973,14(1):104-114
Using the method of forcing of set theory, we prove the following two theorems on the existence of measurable choice functions:
LetT be the closed unit interval [0,1] and letm be the usual Lebesgue measure defined on the Borel subsets ofT. Theorem1. LetS⊂T×T be a Borel set such that for alltεT,S
t
def={x|(t,x)εS} is countable and non-empty. Then there exists a countable series of Lebesgue-measurable functionsf
n: T→T such thatS
t={fn(t)|nεω} for alltε[0,1],W
x={y|(x,y)εW} is uncountable. Then there exists a functionh:[0,1]×[0,1]→W with the following properties: (a) for each xε[0,1], the functionh(x,·) is one-one and ontoW
x and is Borel measurable; (b) for eachy, h(·, y) is Lebesgue measurable; (c) the functionh is Lebesgue measurable. 相似文献
5.
Theω′-topology on the spaceL(X, Y) of bounded linear operators from the Banach spaceX into the Banach spaceY is discussed in [10]. Let ℒw' (X, Y) denote the space of allT∈L(X, Y) for which there exists a sequence of compact linear operators (T
n)⊂K(X, Y) such thatT=ω′−limnTn and let
. We show that
is a Banach ideal of operators and that the continuous dual spaceK(X, Y)* is complemented in
. This results in necessary and sufficient conditions forK(X, Y) to be reflexive, whereby the spacesX andY need not satisfy the approximation property. Similar results follow whenX andY are locally convex spaces.
Financial support from the Potchefstroom University and Maseno University is greatly acknowledged.
Financial support from the NRF and Potchefstroom University is greatly acknowledged. 相似文献
6.
We prove that natural closure operations on quotient structures of the h-quasiorder of finite and (at most) countable k-labeled forests (k ≥ 3) are definable provided that minimal nonsmallest elements are allowed as parameters. This strengthens our previous result
which holds that each element of the h-quasiorder of finite k-labeled forests is definable in the first-order language, and each element of the h-quasiorder of (at most) countable k-labeled forests is definable in the language L
ω1ω; in both cases k ≥ 3 and minimal nonsmallest elements are allowed as parameters. Similar results hold true for two other relevant structures:
the h-quasiorder of finite (resp. countable) k-labeled trees and k-labeled trees with a fixed label on the root element. 相似文献
7.
Given a weighted discrete abelian semigroup (S, ω), the semigroup M
ω
(S) of ω-bounded multipliers as well as the Rees quotient M
ω
(S)/S together with their respective weights [(w)\tilde]\tilde{\omega} and [(w)\tilde]q\tilde{\omega}_q induced by ω are studied; for a large class of weights ω, the quotient l1(Mw(S),[(w)\tilde])/l1(S,w)\ell^1(M_{\omega}(S),\tilde{\omega})/\ell^1(S,{\omega}) is realized as a Beurling algebra on the quotient semigroup M
ω
(S)/S; the Gel’fand spaces of these algebras are determined; and Banach algebra properties like semisimplicity, uniqueness of uniform
norm and regularity of associated Beurling algebras on these semigroups are investigated. The involutive analogues of these
are also considered. The results are exhibited in the context of several examples. 相似文献
8.
Matatyahu Rubin 《Israel Journal of Mathematics》1974,17(4):392-443
LetT be a complete theory of linear order; the language ofT may contain a finite or a countable set of unary predicates. We prove the following results. (i) The number of nonisomorphic
countable models ofT is either finite or 2ω. (ii) If the language ofT is finite then the number of nonisomorphic countable models ofT is either 1 or 2ω. (iii) IfS
1(T) is countable then so isS
n(T) for everyn. (iv) In caseS
1(T) is countable we find a relation between the Cantor Bendixon rank ofS
1(T) and the Cantor Bendixon rank ofS
n(T). (v) We define a class of modelsL, and show thatS
1(T) is finite iff the models ofT belong toL. We conclude that ifS
1(T) is finite thenT is finitely axiomatizable. (vi) We prove some theorems concerning the existence and the structure of saturated models.
Most of the results in this paper appeared in the author’s Master of Science thesis which was prepared at the Hebrew University
under the supervision of Professor H. Gaifman. 相似文献
9.
LetT(t) be the translation group onY=C
0(ℝ×K)=C
0(ℝ)⊗C(K),K compact Hausdorff, defined byT(t)f(x, y)=f(x+t, y). In this paper we give several representations of the sun-dialY
⊙ corresponding to this group. Motivated by the solution of this problem, viz.Y
⊙=L
1(ℝ)⊗M(K), we develop a duality theorem for semigroups of the formT
0(t)⊗id on tensor productsZ⊗X of Banach spaces, whereT
0(t) is a semigroup onZ. Under appropriate compactness assumptions, depending on the kind of tensor product taken, we show that the sun-dial ofZ⊗X is given byZ
⊙⊗X*. These results are applied to determine the sun-dials for semigroups induced on spaces of vector-valued functions, e.g.C
0(Ω;X) andL
p
(μ;X).
This paper was written during a half-year stay at the Centre for Mathematics and Computer Science CWI in Amsterdam. I am grateful
to the CWI and the Dutch National Science Foundation NWO for financial support. 相似文献
10.
V. D. Mazurov 《Algebra and Logic》1997,36(1):23-32
For a finite group G, ω(G) denotes the set of orders of its elements. If ω is a subset of the set of natural numbers, h(ω)
stands for the number of pairwise nonisomorphic finite groups G for which ω(G)=ɛ. We prove that h(ω(G))=1, if G is isomorphic
to S9, S11, S12, S13, or A12, and h(ω(G))=2 if G is isomorphic to S2(6) or to O
8
+
(2). 01
Supported by RFFR grant No. 96-01-01893.
Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 37–53, January–February, 1997. 相似文献
11.
Anders Grimvall 《Stochastic Processes and their Applications》1973,1(4):335-368
Starting from a real-valued Markov chain X0,X1,…,Xn with stationary transition probabilities, a random element {Y(t);t[0, 1]} of the function space D[0, 1] is constructed by letting Y(k/n)=Xk, k= 0,1,…,n, and assuming Y (t) constant in between. Sample tightness criteria for sequences {Y(t);t[0,1]};n of such random elements in D[0, 1] are then given in terms of the one-step transition probabilities of the underlying Markov chains. Applications are made to Galton-Watson branching processes. 相似文献
12.
J. Hounie Rafael Augusto dos Santos Kapp 《Journal of Fourier Analysis and Applications》2009,15(2):153-178
In this work, we study the continuity of pseudodifferential operators on local Hardy spaces h
p
(ℝ
n
) and generalize the results due to Goldberg and Taylor by showing that operators with symbols in S
1,δ
0(ℝ
n
), 0≤δ<1, and in some subclasses of S
1,10(ℝ
n
) are bounded on h
p
(ℝ
n
) (0<p≤1). As an application, we study the local solvability of the planar vector field L=∂
t
+ib(x,t)∂
x
, b(x,t)≥0, in spaces of mixed norm involving Hardy spaces.
Work supported in part by CNPq, FINEP, and FAPESP. 相似文献
13.
Michel Talagrand 《Probability Theory and Related Fields》1998,112(4):545-563
Consider 0<α<1 and the Gaussian process Y(t) on ℝ
N
with covariance E(Y(s)Y(t))=|t|2α+|s|2α−|t−s|2α, where |t| is the Euclidean norm of t. Consider independent copies X
1,…,X
d
of Y and␣the process X(t)=(X
1(t),…,X
d
(t)) valued in ℝ
d
. When kN≤␣(k−1)αd, we show that the trajectories of X do not have k-multiple points. If N<αd and kN>(k−1)αd, the set of k-multiple points of the trajectories X is a countable union of sets of finite Hausdorff measure associated with the function ϕ(ɛ)=ɛ
k
N
/α−(
k
−1)
d
(loglog(1/ɛ))
k
. If N=αd, we show that the set of k-multiple points of the trajectories of X is a countable union of sets of finite Hausdorff measure associated with the function ϕ(ɛ)=ɛ
d
(log(1/ɛ) logloglog 1/ɛ)
k
. (This includes the case k=1.)
Received: 20 May 1997 / Revised version: 15 May 1998 相似文献
14.
U. Luther 《Integral Equations and Operator Theory》2006,54(4):541-554
We study integral operators on (−1, 1) with kernels k(x, t) which may have weak singularities in (x, t) with x ∈N1, t ∈N2, or x=t, where N1,N2 are sets of measure zero. It is shown that such operators map weighted L∞–spaces into certain weighted spaces of smooth functions, where the degree of smoothness is the higher the smoother the kernel
k(x, t) as a function in x is. The spaces of smooth function are generalizations of the Ditzian-Totik spaces which are defined in terms of the errors
of best weighted uniform approximation by algebraic polynomials. 相似文献
15.
Following [5], aT
3 spaceX is called good (splendid) if it is countably compact, locally countable (andω-fair).G(κ) (resp.S(κ)) denotes the statement that a good (resp. splendid) spaceX with |X|=κ exists. We prove here that (i) Con(ZF)→Con(ZFC+MA+2
ω
is big+S(κ) holds unlessω=cf(κ)<κ); (ii) a supercompact cardinal implies Con(ZFC+MA+2suω>ω+1+┐G(ωω+1); (iii) the “Chang conjecture” (ωω+1),→(ω
1,ω) implies ┐S(κ) for allκ≧k≧ωω; (iv) ifP addsω
1 dominating reals toV iteratively then, in
, we haveG(λω) for allλ.
Research supported by Hungarian National Foundation for Scientific Research grant no. 1805. 相似文献
16.
Yu. V. Netrusov 《Journal of Mathematical Sciences》1989,47(6):2871-2881
The paper examines imbeddings of Besov spaces B
E, θ
ω
in ideal spaces (Banach lattices) given that ω ∈ Sk). In particular, the symmetric hull of the space B
E, θ
ω
is described (E is a symmetric space), an inequality of different metrics is obtained, and imbeddings in Orlicz and Lorentz
spaces and in some weighted spaces are studied. Most of the results are easily extended to the anisotropic case.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 159, pp. 69–82, 1987. 相似文献
17.
We obtain asymptotic representations as t ↑ ω, ω ≤ + ∞, for all possible types of P
ω(Y
0, λ
0)-solutions (where Y
0 is zero or ±∞ and −∞ ≤ λ0 ≤ +∞) of nonlinear differential equations y
(n) = α
0
p(t)φ(y), where α
0 ∈ {−1, 1}, p: [a, ω[→]0,+∞[ is a continuous function, and φ is a continuous regularly varying function in a one-sided neighborhood of Y
0. 相似文献
18.
Shang Quan Bu 《数学学报(英文版)》2012,28(1):37-44
We study the well-posedness of the equations with fractional derivative Dαu(t)=Au(t)+f(t)(0 ≤t≤2π),where A is a closed operator in a Banach space X,0α1 and Dα is the fractional derivative in the sense of Weyl.Although this problem is not always well-posed in Lp(0,2π;X) or periodic continuous function spaces Cper([0,2π];X),we show by using the method of sum that it is well-posed in some subspaces of L p(0,2π;X) or C per([0,2π];X). 相似文献
19.
Jackson's Theorem on Bounded Symmetric Domains 总被引:1,自引:0,他引:1
Ming Zhi WANG Guang Bin REN 《数学学报(英文版)》2007,23(8):1391-1404
Polynomial approximation is studied on bounded symmetric domain Ω in C^n for holomorphic function spaces X such as Bloch-type spaces, Bergman-type spaces, Hardy spaces, Ω algebra and Lipschitz space. We extend the classical Jackson's theorem to several complex variables:Eκ(f,X)≤ω(1/k,f,X), where Eκ(f,X) is the deviation of the best approximation of f ∈X by polynomials of degree at most k with respect to the X-metric and ω(1/k,f,X) is the corresponding modulus of continuity. 相似文献
20.
The closed model category of exterior spaces, that contains the proper category, is a useful tool for the study of non compact
spaces and manifolds. The notion of exterior weak ℕ-S-equivalences is given by exterior maps which induce isomorphisms on the k-th ℕ-exterior homotopy groups for k ∈ S, where S is a set of non negative integers. The category of exterior spaces with a base ray localized by exterior weak ℕ-S-equivalences is called the category of exterior ℕ-S-types. The existence of closed model structures in the category of exterior spaces permits to establish equivalences between
homotopy categories obtained by dividing by exterior homotopy relations, and categories of fractions (localized categories)
given by the inversion of classes of week equivalences. The family of neighbourhoods ‘at infinity’ of an exterior space can
be interpreted as a global prospace and under the condition of first countable at infinity we can consider a global tower
instead of a prospace. The objective of this paper is to use localized categories to find the connection between S-types of exterior spaces and S-types of global towers of spaces. The main result of this paper establishes an equivalence between the category of S-types of rayed first countable exterior spaces and the category of S-types of global towers of pointed spaces. As a consequence of this result, categories of global towers of algebraic models
localized up to weak equivalences can be used to give some algebraic models of S-types.
The authors acknowledge the financial support given by the projects FOMENTA 2007/03 and MTM2007-65431. 相似文献