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1.
We prove that a locally compact ANR-space X is a Q-manifold if and only if it has the Disjoint Disk Property (DDP), all points of X are homological Z
∞-points and X has the countable-dimensional approximation property (cd-AP), which means that each map f: K → X of a compact polyhedron can be approximated by a map with the countable-dimensional image. As an application we prove that
a space X with DDP and cd-AP is a Q-manifold if some finite power of X is a Q-manifold. If some finite power of a space X with cd-AP is a Q-manifold, then X
2 and X × [0, 1] are Q-manifolds as well. We construct a countable family χ of spaces with DDP and cd-AP such that no space X ∈ χ is homeomorphic to the Hilbert cube Q whereas the product X × Y of any different spaces X, Y ∈ χ is homeomorphic to Q. We also show that no uncountable family χ with such properties exists.
This work was supported by the Slovenian-Ukrainian (Grant No. SLO-UKR 04-06/07) 相似文献
2.
Paul Arne ?stv?r 《K-Theory》2004,31(4):345-355
Let X be a connected based space and p be a two-regular prime number. If the fundamental group of X has order p, we compute the two-primary homotopy groups of the homotopy fiber of the trace map A(X) → TC(X) relating algebraic K-theory of spaces to topological cyclic homology. The proof uses a theorem of Dundas and an explicit calculation of the cyclotomic
trace map K(ℤ[Cp])→ TC(ℤ[Cp]). 相似文献
3.
S. V. Ludkovsky 《Journal of Mathematical Sciences》2009,157(2):367-385
In this paper, the duality of κ-normed topological vector spaces X is defined and investigated, where X is over the field K = R, or K = C, or a non-Archimedean field. For such spaces, an analog of the Mackey-Arens theorem is proved. The conditional κ-normability of spaces L(X) of linear topological homeomorphisms of a locally convex κ-normed space X is studied, where the image of elements under the corresponding operations is in L(X). Cases where the κ-normability of a topological vector space implies its local convexity are investigated. Applications of κ-normed spaces for resolutions of differential equations and for approximations of functions in mathematical economics are
given.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 52, Functional
Analysis, 2008. 相似文献
4.
LetS be a topological semigroup andAP(S) the space of continous complex almost periodic functions onS. We obtain characterizations of compact and weakly compact operators from a Banach spaceX into AP(S). For this we use the almost periodic compactification ofS obtained through uniform spaces. For a bounded linear operatorT fromX into AP(S), letT
5, be the translate ofT bys inS defined byT
5(x)=(Tx)
5
. We define topologies on the space of bounded linear operators fromX into AP(S) and obtain the necessary and sufficient conditions for an operatorT to be compact or weakly compact in terms of the uniform continuity of the maps→T
5. IfS is a Hausdorff topological semigroup, we also obtain characterizations of compact and weakly compact multipliers on AP(S) in terms of the uniform continuity of the map S→μs, where μs denotes the unique vector measure corresponding to the operatorT
5. 相似文献
5.
Alexander Šostak 《Journal of Mathematical Sciences》2007,144(5):4527-4534
Given an M-valued equality E: X×X → M on a set X, we extend it to the M-valued equality ε: L
X
× L
X
→ M on the L-powerset L
X
of X, where L is a complete sublattice of a GL-monoid M. As a result, we come to a category SET(M,L) whose objects are quadruples (X,E,L
X
, ε). This category serves as a ground category for the category L-TOP(M) of (L,M)-valued topological spaces and some of its subcategories, which are the main subject of this paper. In particular, as special
cases, we obtain here Chang-Goguen, Lowen, Kubiak-Šostak, and some other known categories related to fuzzy topology.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 237–247, 2005. 相似文献
6.
Yu. È. Linke 《Siberian Mathematical Journal》2011,52(3):501-511
Given a continuous sublinear operator P: V → C(X) from a Hausdorff separable locally convex space V to the Banach space C(X) of continuous functions on a compact set X we prove that the subdifferential ∂P at zero is operator-affinely homeomorphic to the compact subdifferential ∂
c
Q, i.e., the subdifferential consisting only of compact linear operators, of some compact sublinear operator Q: ł2 → C(X) from a separable Hilbert space ł2, where the spaces of operators are endowed with the pointwise convergence topology. From the topological viewpoint, this
means that the space L
c
(ł2, C(X)) of compact linear operators with the pointwise convergence topology is universal with respect to the embedding of the subdifferentials
of sublinear operators of the class under consideration. 相似文献
7.
A. K. Katsaras 《P-Adic Numbers, Ultrametric Analysis, and Applications》2009,1(3):190-203
LetX be a Hausdorff zero-dimensional topological space,K(X) the algebra of all clopen subsets of X, E a Hausdorff locally convex space over a non-Archimedean valued field and C
b
(X) the space of all bounded continuous -valued functions on X. The space M(K(X),E), of all bounded finitely-additive measures m: K(X) → E, is investigated. If we equip C
b
(X) with the topologies β
o
, β, β
u
, τ
b
or β
ob
, it is shown that, for E (compete, the corresponding spaces of continuous linear operators from C
b
(X) to E (are algebraically isomorphic to certain subspaces of M(K(X),E).
The text was submitted by the author in English. 相似文献
8.
Joe J. Perez 《Annals of Global Analysis and Geometry》2010,37(1):1-20
Let G be a unimodular Lie group, X a compact manifold with boundary, and M the total space of a principal bundle G → M → X so that M is also a strongly pseudoconvex complex manifold. In this study, we show that if G acts by holomorphic transformations satisfying a local property, then the space of square-integrable holomorphic functions
on M is infinite-dimensional. 相似文献
9.
A Banach space X will be called extensible if every operator E → X from a subspace E ⊂ X can be extended to an operator X → X. Denote by dens X. The smallest cardinal of a subset of X whose linear span is dense in X, the space X will be called automorphic when for every subspace E ⊂ X every into isomorphism T: E → X for which dens X/E = dens X/TE can be extended to an automorphism X → X. Lindenstrauss and Rosenthal proved that c
0 is automorphic and conjectured that c
0 and ℓ2 are the only separable automorphic spaces. Moreover, they ask about the extensible or automorphic character of c
0(Γ), for Γ uncountable. That c
0(Γ) is extensible was proved by Johnson and Zippin, and we prove here that it is automorphic and that, moreover, every automorphic
space is extensible while the converse fails. We then study the local structure of extensible spaces, showing in particular
that an infinite dimensional extensible space cannot contain uniformly complemented copies of ℓ
n
p
, 1 ≤ p < ∞, p ≠ 2. We derive that infinite dimensional spaces such as L
p
(μ), p ≠ 2, C(K) spaces not isomorphic to c
0 for K metric compact, subspaces of c
0 which are not isomorphic to c
0, the Gurarij space, Tsirelson spaces or the Argyros-Deliyanni HI space cannot be automorphic.
The work of the first author has been supported in part by project MTM2004-02635 相似文献
10.
Let X and Y be topological spaces such that an arbitrary mapping f: X → Y for which every preimage f
−1 (G) of a set G open in Y is an F
σ-set in X can be represented in the form of the pointwise limit of continuous mappings f
n
: X → Y. We study the problem of subspaces Z of the space Y for which the mappings f: X → Z possess the same property.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1189–1195, September, 2008. 相似文献
11.
Ján Špakula 《Archiv der Mathematik》2010,95(2):171-178
We prove a “quantified” version of the Weyl–von Neumann theorem, more precisely, we estimate the ranks of approximants to
compact operators appearing in Voiculescu’s theorem applied to commutative algebras. This allows considerable simplifications
in uniform K-homology theory, namely it shows that one can represent all the uniform K-homology classes on a fixed Hilbert space with a fixed *-representation of C
0(X), for a large class of spaces X. 相似文献
12.
In the first two sections, we study when a σ-compact space can be covered by a point-finite family of compacta. The main result in this direction concerns topological vector spaces. Theorem 2.4 implies that if such a space L admits a countable point-finite cover by compacta, then L has a countable network. It follows that if f is a continuous mapping of a σ-compact locally compact space X onto a topological vector space L, and fibers of f are compact, then L is a σ-compact space with a countable network (Theorem 2.10). Therefore, certain σ-compact topological vector spaces do not have a stronger σ-compact locally compact topology.In the last, third section, we establish a result going in the orthogonal direction: if a compact Hausdorff space X is the union of two subspaces which are homeomorphic to topological vector spaces, then X is metrizable (Corollary 3.2). 相似文献
13.
Peter Wong 《manuscripta mathematica》1999,98(2):243-254
Let f,g:X→M be maps between two closed connected orientable n-manifolds where M=G/K is the homogeneous space of left cosets of a compact connected Lie group G by a finite subgroup K. In this note, we obtain a simple formula for the Lefschetz coincidence number L(f,g) in terms of topological degree, generalizing some previously known formulas for fixed points. Our approach, by means of
Nielsen root theory, also allows us to give a simpler and more geometric proof of the fact that all coincidence classes of
f and g have coincidence index of the same sign.
Received: 3 March 1998 / Revised version: 29 June 1998 相似文献
14.
It is proved that if a K?the space λ1(A) is distinguished and E is an arbitrary Fréchet space then every reflexive map T: λ1(A)→E (i.e., T maps bounded sets into relatively weakly compact ones) factorizes through a reflexive Fréchet space. An analogous result
is proved for Montel maps (i.e., which map bounded sets into relatively compact ones). The result is a consequence of the
fact proved also in this paper that, for a distinguished λ1(A) space, the spaces of reflexive maps R(λ1(A), C(K)) and of Montel maps M(λ1(A), C(K)) are the Mackey completions of the spaces of weakly compact and compact maps, respectively. Consequences for spaces of vector-valued
(weakly) continuous functions are also obtained.
Received: 24 November 1997 / Revised version: 14 May 1998 相似文献
15.
M. D. Voisei 《Set-Valued Analysis》2008,16(4):461-476
This paper is primarily concerned with the problem of maximality for the sum A + B and composition L*
ML in non-reflexive Banach space settings under qualifications constraints involving the domains of A, B, M. Here X, Y are Banach spaces with duals X*, Y*, A, B: X ⇉ X*, M: Y ⇉ Y* are multi-valued maximal monotone operators, and L: X → Y is linear bounded. Based on the Fitzpatrick function, new characterizations for the maximality of an operator as well as
simpler proofs, improvements of previously known results, and several new results on the topic are presented.
相似文献
16.
Olena Karlova Volodymyr Maslyuchenko Volodymyr Mykhaylyuk 《Central European Journal of Mathematics》2012,10(3):1042-1053
We investigate the Baire classification of mappings f: X × Y → Z, where X belongs to a wide class of spaces which includes all metrizable spaces, Y is a topological space, Z is an equiconnected space, which are continuous in the first variable. We show that for a dense set in X these mappings are functions of a Baire class α in the second variable. 相似文献
17.
Bangteng Xu 《Journal of Algebraic Combinatorics》2008,27(2):127-141
Sunder and Wildberger (J. Algebr. Comb.
18, 135–151, 2003) introduced the notion of actions of finite hypergroups, and studied maximal irreducible actions and *-actions. One of the
main results of Sunder and Wildberger states that if a finite hypergroup K admits an irreducible action which is both a maximal action and a *-action, then K arises from an association scheme. In this paper we will first show that an irreducible maximal action must be a *-action,
and hence improve Sunder and Wildberger’s result (Theorem 2.9). Another important type of actions is the so-called w-maximal actions. For a w-maximal action π:K→Aff (X), we will prove that π is faithful and |X|≥|K|, and |K| is the best possible lower bound of |X|. We will also discuss the strong connectivity of the digraphs induced by a w-maximal action. 相似文献
18.
Jun Tomiyama 《Acta Appl Math》2009,108(3):561-572
For the homeomorphism C*-algebra A(Σ) arising from a topological dynamical system Σ=(X,σ) where σ is a homeomorphism on an arbitrary compact Hausdorff space X, we first give detailed classification of its closed ideals into four classes. In case when X is a compact metric space, we then determine the conditions when the quotient algebras of A(Σ) become quasidiagonal. The case of A(Σ) itself was treated by M. Pimsner. 相似文献
19.
A. V. Osipov 《Journal of Mathematical Sciences》2008,155(4):624-631
For a subset M of a topological space X, the θ-closure {ie626-01} M is defined as the set of all x ∈ X such that any closed neighborhood of x intersects M. A Urysohn space X is said to be U-closed if, whenever X ∪ {ξ} is a Urysohn space obtained from X by adding one point ξ, the point ξ is isolated in X ∪ {ξ}. The θ-closure operator is applied to study compactness-type properties of (weakly) U-and H-closed and closed-hereditarily U-and H-closed spaces.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 48, General
Topology, 2007. 相似文献
20.
Let X be a Banach space, K be a scattered compact and T: B
C(K) → X be a Fréchet smooth operator whose derivative is uniformly continuous. We introduce the smooth biconjugate T**: B
C(K)** → X** and prove that if T is noncompact, then the derivative of T** at some point is a noncompact linear operator. Using this we conclude, among other things, that either
is compact or that ℓ1 is a complemented subspace of X*. We also give some relevant examples of smooth functions and operators, in particular, a C
1,u
-smooth noncompact operator from B
c
O which does not fix any (affine) basic sequence.
P. Hájek was supported by grants A100190502, Institutional Research Plan AV0Z10190503. 相似文献