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1.
We introduce new classes of sets called Λ
g
-closed sets and Λ
g
-open sets in topological spaces. We also investigate several properties of such sets. It turns out that Λ
g
-closed sets and Λ
g
-open sets are weaker forms of closed sets and open sets, respectively and stronger forms of g-closed sets and g-open sets, respectively.
Dedicated to Professor Maximilian Ganster on the occasion of his 50th birthday 相似文献
2.
Nuclear Köthe sequence spaceλ(P) its crossdualλ(P) x and their non-nuclear variants are examined as topological algebras. Modelling on them, a general theory of nuclear topological algebras with orthogonal basis is developed. As a by-product, abstract characterizations of sequence algebras ?∞ andc 0 are obtained. In a topological algebra set-up, an abstract Grothendieck-Pietsch nuclearity criterion is developed. 相似文献
3.
A. El Kinani 《Rendiconti del Circolo Matematico di Palermo》2004,53(3):407-416
We show that the convexified topology of a locally pseuod-convex algebra can be determined by an explicit family of seminorms.
A natural relationship between some properties of locally pseudo-convex algebras and the associated locally convex algebras
obtained by convexification is also established. 相似文献
4.
On Well-posed Mutually Nearest and
Mutually Furthest Point Problems in Banach Spaces 总被引:3,自引:0,他引:3
ChongLI RenXingNI 《数学学报(英文版)》2004,20(1):147-156
Let G be a non-empty closed(resp.bounded closed)boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X.Let K(X)denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance.Moreover,let KG(X)denote the closure of the set {A∈K(x):A∩G=0}.We prove that the set of all A∈KG(X)(resp.A∈K(X)),such that the minimization (resp.maximization)problem min(A,G)(resp.max(A,G))is well posed,contains a dense Gδ-subset of KG(X)(resp.K(X)).thus extending the recent results due to Blasi,Myjak and Papini and Li. 相似文献
5.
Surjit Singh Khurana 《Mathematica Slovaca》2008,58(3):309-314
X
1 and X
2 are completely regular Hausdorff spaces, E
1, E
2 and F are Dedekind complete Banach lattices, 〈·,·〉: E
1 × E
2 → F is a bilinear mapping, and μ
1 and μ
2 are, respectively, E
1 and E
2 valued positive, countably additive Baire or Borel measures (countable additivity relative to order convergence) on X
1 and X
2. Under certain conditions the existence and uniqueness of the F-valued, positive, product measure is proved.
相似文献
6.
David R. Pitts 《K-Theory》1989,2(6):737-752
In this paper we compute the K
0 group of any nest subalgebra of (). 相似文献
7.
8.
We study actions of the groups ?n and ?n by Lebesgue space automorphisms. We prove that a typical ?n-action can be inserted only in injective actions of ?n, n ∈ ?. We give a simple proof of the fact that a typical ?2-action cannot be inserted in an ?-action. 相似文献
9.
10.
The Szpilrajn theorem and its strengthening by Dushnik and Miller belong to the most quoted theorems in many fields of pure
and applied mathematics as, for instance, order theory, mathematical logic, computer sciences, mathematical social sciences,
mathematical economics, computability theory and fuzzy mathematics. The Szpilrajn theorem states that every partial order
can be refined or extended to a total (linear) order. The theorem by Dushnik and Miller states, moreover, that every partial
order is the intersection of its total (linear) refinements or extensions. Since in mathematical social sciences or, more
general, in any theory that combines the concepts of topology and order one is mainly interested in continuous total orders
or preorders in this paper some aspects of a possible continuous analogue of the Szpilrajn theorem and its strengthening by
Dushnik and Miller will be discussed. In particular, necessary and sufficient conditions for a topological space to satisfy
a possible continuous analogue of the Dushnik-Miller theorem will be presented. In addition, it will be proved that a continuous
analogue of the Szpilrajn theorem does not hold in general. Further, necessary and in some cases necessary and sufficient
conditions for a topological space to satisfy a possible continuous analogue of the Szpilrajn theorem will be presented.
相似文献
11.
A number of generalized metric spaces have been defined or characterized in terms of g-functions. Symmetric g-functions are discussed by C. Good, D. Jennings and A. M. Mohamad. In this paper, some questions about symmetric g-functions are answered, particularly it is shown that every sym-wg-space is expandable.
The project is supported by the NNSF (10571151) and NSF (2006J0397) of Fujian Province of China. 相似文献
12.
Translating the notion of G
δ
-dense and well-embedded subspaces into a pointfree setting gives some elegant results (with remarkably simple proofs), most notably how the two concepts are related – a fact which, no doubt, is well-known to classical topologists, but is easily overlooked. 相似文献
13.
Á. Császár 《Acta Mathematica Hungarica》2008,121(4):395-400
It is shown in the paper [1] that every generalized topology can be generated by a generalized neighbourhood system. Following
the paper [3], we discuss some questions related to this construction.
Research supported by Hungarian Foundation for Scientific Research, grant No. T 49786. 相似文献
14.
In this paper we give a simpler proof of the L
p
-Schwartz space isomorphism (0 < p ≤ 2) under the Fourier transform for the class of functions of left δ-type on a Riemannian symmetric space of rank one. Our treatment rests on Anker’s [2] proof of the corresponding result in
the case of left K-invariant functions on X. Thus we give a proof which relies only on the Paley-Wiener theorem. 相似文献
15.
Ulrich Faigle Walter Kern Boris Spieker 《Mathematical Methods of Operations Research》1996,43(2):239-254
We consider the following game: Two players independently choose a chain in a partially ordered set. How many bits of information have to be communicated until at least one of the players knows whether the chains have exactlyt elements in common? This model generalizes thet-intersection problem for subsets of a finite set. We establish the deterministic communication complexity in general. For the special cases of generalized Boolean algebras, we present improved nondeterministic and probabilistic protocols that are of optimal order of complexity for classes with fixed widthq. 相似文献
16.
P. V. Chernikov 《Siberian Mathematical Journal》2007,48(1):189-190
We establish that condition (Γ) on brick decomposition is indecomposable. This answers K. Borsuk’s question [1]. We prove that there exist metric spaces X and Y and a point (a, b) ∈ X × Y such that (a, b) is an r-point of the product X × Y; moreover, a is not an r-point of X. This answers A. Kosinski’s question [2]. 相似文献
17.
The class of γn-complete hypergroups is introduced. Several properties and examples are found both of γn-complete hypergroups and of KH hypergroups. 相似文献
18.
It is proved by purely algebraic method that weakly conformai, conformai andA
z
3
= 0 are mutually equivalent if ϕ :Ω→ℂP
n
is a non-isotropic harmonic map and the harmonic maps with isotropy order ≥3 are uniquely determined by a system of ordinary
differential equations. A method is given, by which the isotropy orders of non-isotropic harmonic maps can be computed. 相似文献
19.
20.
Á. Császár 《Acta Mathematica Hungarica》2008,120(4):351-354
The paper discusses the generalization of a construction described in [6] for the case when the starting point topology is
replaced by a generalized topology.
Research supported by Hungarian Foundation for Scientific Research, grant No. T 49786. 相似文献