共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
In a set without linear structure equipped with a preorder, we give a general existence result for efficient points. In a topological vector space equipped with a partial order induced by a closed convex cone with a bounded base, we prove another kind of existence result for efficient points; this result does not depend on the Zorn lemma. As applications, we study a solution problem in vector optimization and generalize the Bishop–Phelps theorem to a topological vector space setting by showing that the B-support points of any sequentially complete closed subset A of a topological vector space E is dense in A, where B is any bounded convex subset of E. 相似文献
3.
Hans-Jürgen Bandelt 《Journal of Graph Theory》1989,13(2):215-228
Separation properties for some intrinsic convexities of graphs are investigated. The most natural convexities defined on a graph are the induced path convexity and the geodesic convexity. A set A of vertices is convex with respect to the former convexity if A contains every induced path connecting two vertices of A. In particular, a characterization of those graphs is given in which all such convex sets are the intersections of halfspaces (i.e., convex sets with convex complements). 相似文献
4.
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
5.
Gerald Beer 《Israel Journal of Mathematics》1987,58(2):205-212
IfA andB are closed nonempty sets in a locally convex space, the straight line path fromA toB is defined by the formulaφ(α)=cl (αA+(1−α)B), 0≦α≦1. IfA andB are convex, then continuity of the path with respect to the Hausdorff uniform topology is necessary for both connectedness
and path connectedness ofA toB within the convex sets so topologized. We also produce internal necessary and sufficient conditions for continuity of the
path between pairs of convex sets. 相似文献
6.
In the context of vector optimization and generalizing cones with bounded bases, we introduce and study quasi-Bishop-Phelps cones in a normed space X. A dual concept is also presented for the dual space X*. Given a convex subset A of a normed space X partially ordered by a closed convex cone S with a base, we show that, if A is weakly compact, then positive proper efficient points are sequentially weak dense in the set E(A, S) of efficient points of A; in particular, the connotation weak dense in the above can be replaced by the connotation norm dense if S is a quasi-Bishop-Phelps cone. Dually, for a convex subset of X* partially ordered by the dual cone S
+, we establish some density results of positive weak* efficient elements of A in E(A, S
+). 相似文献
7.
A shadow of a subset A of Rn is the image of A under a projectiononto a hyperplane. Let C be a closed nonconvex set in Rn suchthat the closures of all its shadows are convex. If, moreover,there are n independent directions such that the closures ofthe shadows of C in those directions are proper subsets of therespective hyperplanes then it is shown that C contains a copyof Rn2. Also for every closed convex set B minimalimitations C of B are constructed, that is, closed subsetsC of B that have the same shadows as B and that are minimalwith respect to dimension. 相似文献
8.
Simeon Reich 《Journal of Functional Analysis》1977,26(4):378-395
This paper contains both negative and positive results concerning the possibility of extending accretive sets in Banach spaces to m-accretive sets. On the one hand, it is shown that if a closed convex subset C of a reflexive strictly convex Banach space E is not a nonexpansive retract of E, then no accretive A such that clco(D(A)) = C can be extended to an m-accretive set B with D(B) ?C, and that if a non-Hilbert E is reflexive and smooth, then there is an accretive set A ?E × E which has no m-accretive extension. On the other hand, we establish positive results and then apply them to the study of the asymptotic behavior of nonlinear semigroups, the construction of zeros of accretive sets, and the characterization of invariant sets for nonlinear semigroups. 相似文献
9.
We determine the maximal value ofr with the following property. If the convex hull of a set inR
2 contains a unit circleB, then a subset of at most four points can be selected so that the convex hull of this subset contains the circle of radiusr concentric withB. That the result is sharp is shown by the example when the original set is the set of vertices of a regular pentagon circumscribed
aroundB.
Imre Bárány was partially supported by Hungarian National Science Foundation Grant Nos. 1907 and 1909. Aladár Heppes was partially
supported by Hungarian National Science Foundation Grant No. 2583. 相似文献
10.
Michael Kallay 《Geometriae Dedicata》1984,16(1):1-16
A point r is a Radon point of a finite set S if r=conv Aconv B, where A and B are disjoint subsets of S. Two characterizations are given for those finite sets in R
d
which contain their Radon points, and the convex hull of such a set is described. 相似文献
11.
Kensaku Gomi 《Logica Universalis》2009,3(2):243-291
A logical space is a pair (A, B){(A, {\mathcal{B}})} of a non-empty set A and a subset B{{\mathcal{B}}} of P A{{\mathcal{P}} A} . Since P A{{\mathcal{P}} A} is identified with {0, 1}A and {0, 1} is a typical lattice, a pair (A, F){(A, {\mathcal{F}})} of a non-empty set A and a subset F{{\mathcal{F}}} of
\mathbbBA{{\mathbb{B}}^A} for a certain lattice
\mathbbB{{\mathbb{B}}} is also called a
\mathbbB{{\mathbb{B}}} -valued functional logical space. A deduction system on A is a pair (R, D) of a subset D of A and a relation R between A*
and A. In terms of these simplest concepts, a general framework for studying the logical completeness is constructed. 相似文献
12.
The problem of confining the trajectory of a linear discrete-time system in a given polyhedral domain is addressed through the concept of (A, B)-invariance. First, an explicit characterization of (A, B)-invariance of convex polyhedra is proposed. Such characterization amounts to necessary and sufficient conditions in the form of linear matrix relations and presents two major advantages compared to the ones found in the literature: it applies to any convex polyhedron and does not require the computation of vertices. Such advantages are felt particularly in the computation of the supremal (A, B)-invariant set included in a given polyhedron, for which a numerical method is proposed. The problem of computing a control law which forces the system trajectories to evolve inside an (A, B)-invariant polyhedron is treated as well. Finally, the (A, B)-invariance relations are generalized to persistently disturbed systems. 相似文献
13.
We prove that affine straight lineϕ
A,B(t)=(1−t)A+tB going through bounded closed convex setsA andB is not injective if and only ifA−B is symmetric andA−A,B−B are homotetic. 相似文献
14.
Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces
S. Takahashi W. Takahashi M. Toyoda 《Journal of Optimization Theory and Applications》2010,147(1):27-41
Let C be a closed and convex subset of a real Hilbert space H. Let T be a nonexpansive mapping of C into itself, A be an α-inverse strongly-monotone mapping of C into H and let B be a maximal monotone operator on H, such that the domain of B is included in C. We introduce an iteration scheme of finding a point of F (T)∩(A+B)−10, where F (T) is the set of fixed points of T and (A+B)−10 is the set of zero points of A+B. Then, we prove a strong convergence theorem, which is different from the results of Halpern’s type. Using this result, we
get a strong convergence theorem for finding a common fixed point of two nonexpansive mappings in a Hilbert space. Further,
we consider the problem for finding a common element of the set of solutions of a mathematical model related to equilibrium
problems and the set of fixed points of a nonexpansive mapping. 相似文献
15.
Bierstedt and Bonet proved in 1988 that if a metrizable locally convex space E satisfies the Heinrich's density condition, then every bounded set in the strong dual (E ′, β (E ′, E)) of E is metrizable; consequently E is distinguished, i.e. (E ′, β (E ′, E)) is quasibarrelled. However there are examples of distinguished Fréchet spaces whose strong dual contains nonmetrizable bounded sets. We prove that a metrizable locally convex space E is distinguished iff every bounded set in the strong dual (E ′, β (E ′, E)) has countable tightness, i.e. for every bounded set A in (E ′, β (E ′, E)) and every x in the closure of A there exists a countable subset B of A whose closure contains x. This extends also a classical result of Grothendieck. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
Let A, B be two archimedean ℓ-algebras and let U,V be two positive linear maps from A to B. We call that the couple (U,V) is separating with respect to A and B if |a||b| = 0 in A implies |U (a)||V (b)| = 0 in B. In this paper, we prove that if A is an f-algebra with unit elment e, if B is an ℓ-algebra and if (U,V) is a separating couple with respect to A and B then (U
∼∼,V
∼∼), where U
∼∼ (resp V
∼∼) is the bi-adjoint of U (resp of V), is again a separating couple with respect to the order continuous order biduals (A′)′
n
and (B′)′
n
of A and B respectively furnished with their Arens products respectively. Moreover, in the case where B′ separates the points of B, we give a characterization of any separating couple with respect to A and B.
相似文献
17.
Let A and B be given convex closed bounded nonempty subsets in a Hilbert space H; let the first player choose points in the set A and let the second one do those in the set B. We understand the payoff function as the mean value of the distance between these points. The goal of the first player is
to minimize the mean value, while that of the second player is to maximize it. We study the structure of optimal mixed strategies
and calculate the game value. 相似文献
18.
Thomas Landes 《Archiv der Mathematik》1981,37(1):248-255
In this note it is proved that a subsetA of a locally convex topological vector spaceE has normal structure with respect to every continuous seminorm onE — called totally normal structure — iff every bounded convex subset ofA is precompact. Some consequences are discussed. 相似文献
19.
Li Xin CHENG Yan Mei TENG 《数学学报(英文版)》2007,23(6):1063-1066
To guarantee every real-valued convex function bounded above on a set is continuous, how "thick" should the set be? For a symmetric set A in a Banach space E,the answer of this paper is: Every real-valued convex function bounded above on A is continuous on E if and only if the following two conditions hold: i) spanA has finite co-dimentions and ii) coA has nonempty relative interior. This paper also shows that a subset A C E satisfying every real-valued convex function bounded above on A is continuous on E if (and only if) every real-valued linear functional bounded above on A is continuous on E, which is also equivalent to that every real-valued convex function bounded on A is continuous on E. 相似文献
20.
In this paper we define a degenerateC
F-set in PG (2,q
2) as the set of points of intersection of corresponding lines under a suitable collineation between two pencils of lines with
vertices two distinct pointsA andB mapping the lineA ∨B onto itself. We prove that every such a set is the union of the lineA ∨B and a Baer subplane and vice versa every Baer subplane can be seen as a subset of a degenerateC
F-set. 相似文献