共查询到20条相似文献,搜索用时 31 毫秒
1.
We provide proper mapping-characterizations of some embedding-like properties weaker than -embedding. For instance, we show that a subset A of a space X is -embedded in X if and only if for every continuous map g: A → Y into a Banach space Y of weight w(Y) ⩽ λ, there exists a continuous set-valued mapping φ of X into the nonempty compact subsets of Y such that g is a selection for φ∣A (i.e., g(x) ∈ φ(x) for every x ∈ A). On the other hand, we show that a subset A is C*-embedded in X if and only if for every continuous set-valued mapping φ of X into the non-empty compact subsets of a Banach space Y, every continuous selection g: A → Y for φ∣A is continuously extendable to the whole of X. Combining both results we get the well-known mapping-characterization of -embedding which makes more transparent the relation ‘’. Other weak components of -embedding are described in terms of expansions and selections, possible applications are demonstrated as well. 相似文献
2.
Let
be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of
is provided when
is nef but not big, and when a suitable positive multiple of
defines a morphism X → B with connected fibers onto a smooth projective curve B, where KX is the canonical bundle of X. As an application, the case where the genus of B is positive and
has a global section whose zero locus is a smooth hyperelliptic curve of genus ≧ 2 is investigated, and our previous result
is improved for threefolds.
Received: 27 January 2005; revised: 26 March 2005 相似文献
3.
Vladislav Kargin 《Probability Theory and Related Fields》2007,139(3-4):397-413
Let X
i
denote free identically-distributed random variables. This paper investigates how the norm of products behaves as n approaches infinity. In addition, for positive X
i
it studies the asymptotic behavior of the norm of where denotes the symmetric product of two positive operators: . It is proved that if EX
i
= 1, then is between and c
2
n for certain constant c
1 and c
2. For it is proved that the limit of exists and equals Finally, if π is a cyclic representation of the algebra generated by X
i
, and if ξ is a cyclic vector, then for all n. These results are significantly different from analogous results for commuting random variables. 相似文献
4.
Manuela Sobral 《Applied Categorical Structures》1996,4(1):97-106
The paper deals with (effective) descent morphisms for subfibrations
X of the basic fibration Top/X, for topological spaces X and classes
of continuous functions stable under pullback. For a category with pullbacks, we prove the stability under pullback of effective
-descent morphisms for a class
satisfying some suitable conditions. This plays a rôle in relating effective
-descent to effective global-descent and enables us to obtain a criterion for effective étale-descent. We also show that the inclusion of the class of effective global-descent maps in the class surjective effective étale-descent is strict.Partial financial support by Centro de Matemática da Universidade de Coimbra is gratefully acknowledged. 相似文献
5.
John K. McVey 《Archiv der Mathematik》2006,87(2):97-103
When G is a finite nonabelian group, we associate the common-divisor graph with G by letting nontrivial degrees in cd(G) = {χ(1) | χ∈Irr(G)} be the vertices and making distinct vertices adjacent if they have a common nontrivial divisor. A set
of vertices for this graph is said to be strongly connective for cd(G) if there is some prime which divides every member of
, and every vertex outside of
is adjacent to some member of
. When G is nonsolvable, we provide sufficiency conditions for cd(G) to have a strongly connective subset. We also extend a previously known result about groups with nonabelian solvable quotients,
and prove for arbitrary groups G that if the associated graph is connected and has a diameter bounded by 2, then indeed cd(G) has a strongly connective subset. The major focus is on when the derived subgroup G′ is perfect.
Received: 23 July 2005 相似文献
6.
A space X is said to have property (USC) (resp. (LSC)) if whenever is a sequence of upper (resp. lower) semicontinuous functions from X into the closed unit interval [0,1] converging pointwise to the constant function 0 with the value 0, there is a sequence of continuous functions from X into [0,1] such that fn?gn (n∈ω) and converges pointwise to 0. In this paper, we study spaces having these properties and related ones. In particular, we show that (a) for a subset X of the real line, X has property (USC) if and only if it is a σ-set; (b) if X is a space of non-measurable cardinal and has property (LSC), then it is discrete. Our research comes of Scheepers' conjecture on properties S1(Γ,Γ) and wQN. 相似文献
7.
Chun-Gil Park 《Bulletin of the Brazilian Mathematical Society》2005,36(3):333-362
Let X and Y be vector spaces. It is shown that a mapping f : X → Y satisfies the functional equation
if and only if the mapping f : X → Y is additive, and prove the Cauchy–Rassias stability of the functional equation (‡) in Banach modules over a unital C*-algebra. Let
and
be unital C*-algebras, Poisson C*-algebras, Poisson JC*-algebras or Lie JC*-algebras. As an application, we show that every almost homomorphism h :
→
of
into
is a homomorphism when h((d + 2)nuy) = h((d + 2)nu)h(y) or h((d + 2)nu ∘ y) = h((d + 2)nu) ∘ h(y) for all unitaries u ∈
, all y ∈
, and n = 0, 1, 2, • • • .
Moreover, we prove the Cauchy–Rassias stability of homomorphisms in C*-algebras, Poisson C*-algebras, Poisson JC*-algebras or Lie JC*-algebras.
Supported by Korea Research Foundation Grant KRF-2004-041-C00023. 相似文献
(‡) |
8.
Suppose ψ : [0, ∞) → [1, ∞) is a strictly increasing function. A Banach space X is said to have the ψ-Daugavet Property if
the inequality
holds for every compact operator T : X → X. We show that, if 1 < p < ∞ and K(ℓp)↪ X ↪ B(ℓp), then X has the ψ-Daugavet Property with
(here
and cp is an absolute constant). We also prove that a C*-algebra A is commutative if and only if
for any
. Together, these results allow us to distinguish between some types of von Neumann algebras by considering spaces of operators
on them.
The author was supported in part by the NSF grant DMS-9970369. 相似文献
9.
Prof. Ottmar Loos 《Monatshefte für Mathematik》1978,86(2):107-129
Every Jordan pair
defines an algebraic varietyX containing
as a dense open subset.X is projective (affine) if and only if
is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of
. If
is separable then the automorphism group ofX is the projective group of
. 相似文献
10.
Michael Capalbo 《Combinatorica》2005,25(4):379-391
Here we solve an open problem considered by various researchers by presenting the first explicit constructions of an infinite
family
of bounded-degree ‘unique-neighbor’ concentrators Γ; i.e., there are strictly positive constants α and ε, such that all Γ = (X,Y,E(Γ)) ∈
satisfy the following properties. The output-set Y has cardinality
times that of the input-set X, and for each subset S of X with no more than α|X| vertices, there are at least ε|S| vertices in Y that are adjacent in Γ to exactly one vertex in S. Also, the construction of
is simple to specify, and each
has fewer than
edges. We then modify
to obtain explicit unique-neighbor concentrators of maximum degree 3.
* Supported by NSF grant CCR98210-58 and ARO grant DAAH04-96-1-0013. 相似文献
11.
12.
We present a topological analogue of the classic Kadec Renorming Theorem, as follows. Let be two separable metric topologies on the same set X. We prove that every point in X has an -neighbourhood basis consisting of sets that are -closed if and only if there exists a function φ: X→ℝ that is -lower semi-continuous and such that is the weakest topology on X that contains and that makes φ continuous. An immediate corollary is that the class of almost n-dimensional spaces consists precisely of the graphs of lower semi-continuous functions with at most n-dimensional domains. 相似文献
13.
The note contains two examples of function spaces
C
p
(X) endowed with the pointwise topology. The
first example is C
p
(M), M
being a planar continuum, such that C
p
(M)
m
is
uniformly homeomorphic to C
p
(M)
n
if and only if
m = n. This strengthens earlier results concerning
linear homeomorphisms. The second example is a non-Lindelöf function
space C
p
(X), where X is a
monolithic perfectly normal compact space all linearly orderable closed
subspaces of which are metrizable. This example is obtained under the
additional set-theoretical axiom . This solves a problem of Arhangelskiĭ. 相似文献
14.
Vladimir V. Tkachuk 《Quaestiones Mathematicae》2018,41(6):729-743
We present a study of two versions of the point-picking game defined by Berner and Juhasz. Given a space X there are two rivals O and P who take turns playing on X. In the n-th round Player O takes a non-empty open subset Un of the space X and P responds by choosing a point xn ∈ Un. After ω-many moves are completed, the family is called the play of the game. In the CD-game CD(X) Player P wins if the set is closed and discrete. Otherwise O is the winner. In the CL-game CL(X, p), where the point p ∈ X is fixed, Player O wins if contains p in its closure. If , then P is declared to be the winner. We show that in spaces Cp(X) both CD-game and CL-game are equivalent to Gruenhage’s W-game for Player O. If , then Player O has a winning strategy in CL(X, p). The converse is not always true. However, if X is separable or compact of π-weight ≤ ω1, then existence of a winning strategy for O in CL(X, p) is equivalent to . 相似文献
15.
《Quaestiones Mathematicae》2013,36(5):593-604
AbstractLet X be a topological space and Cc(X) be the functionally countable subalgbera of C(X). We call X to be a countably uniform closed-space, briefly, a CU C-space, if Cc(X) is closed under uniform convergence. We investigate that countably uniform closedness need not closed under finite intersection and infinite product. It is shown that if X is a countable union of quasi-components, then X is a CU C-space. We characterize Cc-embedding and also -embedding in CU C-spaces. A subset S of X is called Zc-embedded, if each Z ∈ Zc(S) is the restriction of a zero-set of Zc(X). It is observed that in a zero-dimensional CU C-space, each Lindelöf subspae is Zc-embedded. Moreover, it is shown that in CU C-spaces, each Lindelöf subspace is Cc-embedded if and only if it is c-completely separated from each zero-set, which is disjoint from it. Also in latter spaces, it is observed that for each S ? X, Cc-embedding, -embedding and Zc-embedding coincide, when S belongs to Zc(X) or it is a c-pseudocompact space. Finally, when X is both a CU C-space and a CP-space, then each Zc-embedded subspace is Cc-embedded (-embedded) in X. 相似文献
16.
A metric space (X,d) is called an Atsuji space if every real-valued continuous function on (X,d) is uniformly continuous. It is well known that an Atsuji space must be complete. A metric space (X,d) is said to have an Atsuji completion if its completion is an Atsuji space. In this paper, we study twenty-nine equivalent characterisations for a metric space to have an Atsuji completion. 相似文献
17.
Hueytzen J. Wu 《Topology and its Applications》2006,153(8):1291-1301
By a characterization of compact spaces in Section 1, a process of obtaining a compactification (X∗,k) of an arbitrary topological space X is described in Section 2 by a combined approach of nets and open filters. The Wallman compactification can be embedded in X∗ if X is Hausdorff and by a little modification, the compactification of X is the Stone-?ech compactification of X if X is Tychonoff. 相似文献
18.
A Gaussian t-design is defined as a finite set X in the Euclidean space ℝn satisfying the condition:
for any polynomial f(x) in n variables of degree at most t, here α is a constant real number and ω is a positive weight function on X. It is easy to see that if X is a Gaussian 2e-design in ℝn, then
. We call X a tight Gaussian 2e-design in ℝn if
holds. In this paper we study tight Gaussian 2e-designs in ℝn. In particular, we classify tight Gaussian 4-designs in ℝn with constant weight
or with weight
. Moreover we classify tight Gaussian 4-designs in ℝn on 2 concentric spheres (with arbitrary weight functions). 相似文献
19.
We introduce a notion of energy for harmonic currents of bidegree (1, 1) on a complex K?hler manifold (M, ω). This allows us to define
for positive harmonic currents. We then show that for a lamination with singularities of a compact set in
without directed positive closed currents, there is a unique positive harmonic current which minimizes energy. If X is a compact laminated set in
of class
it carries a unique positive harmonic current T of mass 1. The current T can be obtained by an Ahlfors type construction starting with an arbitrary leaf of X. When X has a totally disconnected set of singularities, contained in a countable union of analytic sets, the above construction
still gives positive harmonic currents.
Received: February 2004 Revision: December 2004 Accepted: June 2005 相似文献
20.
E. Izadi 《Geometriae Dedicata》2005,116(1):87-109
We introduce deformation theoretic methods for determining when a curve X in a nonhyperelliptic Jacobian JC will deform with JC to a non-Jacobian. We apply these methods to a particular class of
curves in the second symmetric power
of C. More precisely, given a pencil
of degree d on C, let X be the curve parametrizing pairs of points in divisors of
(see the paper for the precise scheme-theoretical definition). We prove that if X deforms infinitesimally out of the Jacobian locus with JC then either d=4 or d=5, dim H°
and C has genus 4
This material is based upon work partially supported by the National Security Agency under Grant No. MDA904-98-1-0014 and
the National Science Foundation under Grant No. DMS-0071795. Any opinions, findings and conclusions or recomendations expressed
in this material are those of the author and do not necessarily reflect the views of the National Science Foundation (NSF)
or the National Security Agency (NSA) 相似文献