共查询到20条相似文献,搜索用时 15 毫秒
1.
C. R. J. Clapham 《Periodica Mathematica Hungarica》1987,18(4):317-318
2.
Jachymski showed that the set $$\left\{ {(x,y) \in {{\rm{c}}_0} \times {{\rm{c}}_0}:\left( {\sum\limits_{i = 1}^n {\alpha (i)x(i)y(i)} } \right)_{n = 1}^\infty {\rm{ is bounded}}} \right\}$$ is either a meager subset of c 0 × c 0 or is equal to c 0 × c 0. In the paper we generalize this result by considering more general spaces than c 0, namely C 0(X), the space of all continuous functions which vanish at infinity, and C b (X), the space of all continuous bounded functions. Moreover, we replace the meagerness by σ-porosity. 相似文献
3.
Fred Buckley 《Journal of Graph Theory》1980,4(4):383-387
We consider the problem of which graph invariants have a certain property relating to Ramsey's theorem. Invariants which have this property are called Ramsey functions. We examine properties of chains of graphs associated with Ramsey functions. Methods are developed which enable one to prove that a given invariant is not a Ramsey function. Results for several familiar invariants are presented. 相似文献
4.
The following theorem is proved: Let G be a finite graph with cl(G) = m, where cl(G) is the maximum size of a clique in G. Then for any integer r ≥ 1, there is a finite graph H, also with cl(H) = m, such that if the edges of H are r-colored in any way, then H contains an induced subgraph G′ isomorphic to G with all its edges the same color. 相似文献
5.
This is a study of the dual space of continuous linear functionals on the function space Cps(X) with a natural norm inherited from a larger Banach space. Here ps denotes the pseudocompact-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X. The lattice structure and completeness of this dual space have been studied. Since this dual space is inherently related
to a space of measures, the measure-theoretic characterization of this dual space has been studied extensively. Due to this
characterization, a special kind of topological space, called pz-space, has been studied. Finally the separability of this dual space has been studied.
相似文献
6.
微分方程X=Q(X,Y),Y=P(X)的极限环的存在性 总被引:1,自引:0,他引:1
ФИЛИППОВ在文(1)中,利用变换Lienard方程dx/dy=y-F(x),dy/dt=-g(x)在左右两平面上的轨线新方程在右半平面内的积分线的方法,得到了在一定条件下,方程(1)存在极限环的结论,本文应用文(1)的方法,对类型更为广泛的方程dx/dy=Q(x,y),dy/dt=P(x)进行了探讨,得到了(2)存在稳定极限环的充分条件。 相似文献
7.
8.
9.
A family of sequences has the Ramsey property if for every positive integerk, there exists a least positive integerf
(k) such that for every 2-coloring of {1,2, ...,f
(k)} there is a monochromatick-term member of . For fixed integersm > 1 and 0 q < m, let q(m) be the collection of those increasing sequences of positive integers {x
1,..., xk} such thatx
i+1 – xi q(modm) for 1 i k – 1. Fort a fixed positive integer, denote byA
t
the collection of those arithmetic progressions having constant differencet. Landman and Long showed that for allm 2 and 1 q < m,
q(m) does not have the Ramsey property, while
q(m)
A
m
does. We extend these results to various finite unions of
q(m)
's andA
t
's. We show that for allm 2,
q=1
m–1
q(m) does not have the Ramsey property. We give necessary and sufficient conditions for collections of the form
q(m)
(
t T
A
t) to have the Ramsey property. We determine when collections of the form a(m1) b(m2) have the Ramsey property. We extend this to the study of arbitrary finite unions of q(m)'s. In all cases considered for which has the Ramsey property, upper bounds are given forf
. 相似文献
10.
Dana Bartošová Jordi Lopez-Abad Martino Lupini Brice Mbombo 《Comptes Rendus Mathematique》2017,355(12):1242-1246
We show that the class of finite-dimensional Banach spaces and the class of finite-dimensional Choquet simplices have the Ramsey property. As an application, we show that the group of surjective linear isometries of the Gurarij space is extremely amenable, and that the canonical action is the universal minimal flow of the group of affine homeomorphisms of the Poulsen simplex . This answers questions of Melleray–Tsankov and Conley–Törnquist. 相似文献
11.
A. Tsarpalias 《Proceedings of the American Mathematical Society》1999,127(2):583-587
An elementary setting of the classical Ramsey property is given, which leads to simple proofs of the relevant theorems of Galvin-Prikry and Silver.
12.
Charles Garnet Cox 《代数通讯》2019,47(3):978-989
13.
14.
Summary In this article the zero-divisor graph Γ(C(X)) of the ring C(X) is studied. We associate the ring properties of C(X), the graph properties of Γ(C(X)) and the topological properties of X. Cycles in Γ(C(X)) are investigated and an algebraic and a topological characterization is given for the graph Γ(C(X)) to be triangulated or hypertriangulated. We have shown that the clique number of Γ(C(X)), the cellularity of X and the Goldie dimension of C(X) coincide. It turns out that the dominating number of Γ(C(X)) is between the density and the weight of X. Finally we have shown that Γ(C(X)) is not triangulated and the set of centers of Γ(C(X)) is a dominating set if and only if the set of isolated points of X is dense in X if and only if the socle of C(X) is an essential ideal. 相似文献
15.
Péter Komjáth 《Journal of Graph Theory》2020,94(4):499-508
For every infinite cardinal λ and 2 ≤ n < ω there is a directed graph D of size λ such that D does not contain directed circuits of length ≤n and if its vertices are colored with <λ colors, then there is a monochromatic directed circuit of length n + 1. For every infinite cardinal λ and finite graph X there is a λ-sized graph Y such that if the vertices of Y are colored with <λ colors, then there is a monochromatic induced copy of X. Further, Y does not contain larger cliques or shorter odd circuits than X. The constructions are using variants of Specker-type graphs. 相似文献
16.
Let G be a locally compact group with a fixed right Haar measure andX a separable Banach space. LetL
p
(G, X) be the space of X-valued measurable functions whose norm-functions are in the usualL
p
. A left multiplier ofL
p
(G, X) is a bounded linear operator onB
p
(G, X) which commutes with all left translations. We use the characterization of isometries ofL
p
(G, X) onto itself to characterize the isometric, invertible, left multipliers ofL
p
(G, X) for 1 ≤p ∞,p ≠ 2, under the assumption thatX is not thel
p
-direct sum of two non-zero subspaces. In fact we prove that ifT is an isometric left multiplier ofL
p
(G, X) onto itself then there existsa y ∃ G and an isometryU ofX onto itself such thatTf(x) = U
(R
y
f)(x). As an application, we determine the isometric left multipliers of L1 ∩L
p
(G, X) and L1 ∩C
0
(G, X) whereG is non-compact andX is not the lp-direct sum of two non-zero subspaces. If G is a locally compact abelian group andH is a separable Hubert space, we define
where г is the dual group of G. We characterize the isometric, invertible, left multipliers ofA
p
(G, H), provided G is non-compact. Finally, we use the characterization of isometries ofC(G, X) for G compact to determine the isometric left multipliers ofC(G, X) providedX
*
is strictly convex. 相似文献
17.
This paper studies Weyl's theorems, and some related results for operators with Dunford's property (C). Weyl's theorem in some classes of operators (e.g.M-hyponormal,p-hyponormal and totally paranormal operators) is considered. 相似文献
18.
《Discrete Mathematics》2019,342(4):1089-1097
Given integers , a family of sets satisfies the property if among any members of it some intersect. We prove that for any fixed integer constants , a family of -intervals satisfying the property can be pierced by points, with constants depending only on and . This extends results of Tardos, Kaiser and Alon for the case , and of Kaiser and Rabinovich for the case . We further show that similar bounds hold in families of subgraphs of a tree or a graph of bounded tree-width, each consisting of at most connected components, extending results of Alon for the case . Finally, we prove an upper bound of on the fractional piercing number in families of -intervals satisfying the property, and show that this bound is asymptotically sharp. 相似文献
19.
J. M. Domínguez 《Acta Mathematica Hungarica》2002,95(1-2):29-35
Let
be the algebra of all real-valued continuous functions on a completely regular space X, and
the subalgebra of bounded functions. We show that the space of real maximal ideals of an intermediate algebra between
and
is a
-embedded closed subspace of the product of
with a product of copies of the real line. We make use of this embedding to provide a new characterization of the intermediate algebras that are closed under countable composition, and to exhibit an example of an intermediate algebra on
that is closed under countable composition but not isomorphic to any
. 相似文献
20.
Dedicated to Professor H. G. Tillmann on the occasion of his 65th birthday 相似文献