共查询到20条相似文献,搜索用时 0 毫秒
1.
We describe the semilattice of ordered compactifications of X × Y smaller than o
X × o
Y where X and Y are certain totally ordered topological spaces, and where o
Z denotes the Stone–ech ordered- or Nachbin-compactification of Z. These basic cases are used to illustrate techniques for describing the semilattice of ordered compactifications of X × Y smaller than o
X × o
Y for arbitrary totally ordered topological spaces X and Y. Such products X × Y provide many counterexamples in the theory of ordered compactifications. 相似文献
2.
H. D. Junghenn 《Transactions of the American Mathematical Society》1996,348(3):1051-1073
A weakly continuous, equicontinuous representation of a semitopological semigroup on a locally convex topological vector space gives rise to a family of operator semigroup compactifications of , one for each invariant subspace of . We consider those invariant subspaces which are maximal with respect to the associated compactification possessing a given property of semigroup compactifications and show that under suitable hypotheses this maximality is preserved under the formation of projective limits, strict inductive limits and tensor products.
3.
Piotr Mikołaj Sołtan 《Algebras and Representation Theory》2006,9(6):581-591
Given a discrete quantum group we construct a Hopf -algebra which is a unital -subalgebra of the multiplier algebra of . The structure maps for are inherited from and thus the construction yields a compactification of which is analogous to the Bohr compactification of a locally compact group. This algebra has the expected universal property with respect to homomorphisms from multiplier Hopf algebras of compact type (and is therefore unique). This provides an easy proof of the fact that for a discrete quantum group with an infinite dimensional algebra the multiplier algebra is never a Hopf algebra.Partially supported by Komitet Badań Naukowych grants 2P03A04022 & 2P03A01324, the Foundation for Polish Science and Deutsche Forschungsgemeinschaft. 相似文献
4.
5.
宋士奇 《应用数学学报(英文版)》1994,10(3):225-232
COMPACTIFICATIONSOFBANACHSPACESANDCONSTRUCTIONOFDIFFUSIONPROCESSESSONGSHIQI(宋士奇)(InstituteofAppliedMathematics,theChineseAcad... 相似文献
7.
8.
Alex Chigogidze 《Proceedings of the American Mathematical Society》2000,128(7):2187-2190
We show that for each countable simplicial complex the following conditions are equivalent:
- iff for any space .
- There exists a -invertible map of a metrizable compactum with onto the Hilbert cube.
9.
We prove asymptotic formulas for the number of rational points of bounded height on certain equivariant compactifications of the affine plane. 相似文献
10.
Anneliese Schauerte 《Applied Categorical Structures》2006,14(3):259-272
The category of coherent biframes is shown to be equivalent to that of the coupled lattices, and dually equivalent to the spectral bispaces. Stably continuous biframes arise as the retracts of the coherent biframes. The coherent and the stably continuous biframes are coreflective in all biframes. Weak local compactness is introduced, and in conjunction with regularity, is shown to be sufficient for the construction of smallest compactifications. 相似文献
11.
Some graphs admit drawings in the Euclidean plane (k-space) in such a (natural) way, that edges are represented as line segments of unit length. We say that they have the unit distance property.The influence of graph operations on the unit distance property is discussed. It is proved that the Cartesian product preserves the unit distance property in the Euclidean plane, while graph union, join, tensor product, strong product, lexicographic product and corona do not. It is proved that the Cartesian product preserves the unit distance property also in higher dimensions. 相似文献
12.
Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra, ln this paper, we characterize the projectivity (injectivity) of M as a left A#σ H-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σ H, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative. 相似文献
13.
D. Junghenn 《Semigroup Forum》2008,66(2):328-336
Abstract. Let
be a semidirect product of semitopological semigroups S and T . If S and T act on topological spaces X and Y , respectively, then under suitable conditions there is a natural action of
on X × Y . In this paper we characterize the almost periodic and strongly almost periodic compactification of the flow
,
in terms of related compactifications of (S,X) and (T,Y) . 相似文献
14.
Benoît Kloeckner 《Geometriae Dedicata》2006,117(1):161-180
Real-analytic actions of SL(2;R) on surfaces have been classified, up to analytic change of coordinates. In particular it
is known that there exists countably many analytic equivariant compactification of the isometric action on the hyperbolic
plane. In this paper we study the algebraicity of these actions. We get a classification of the algebraic actions of SL(2,R)
on surfaces. In particular, we classify the algebraic equivariant compactifications of the hyperbolic plane.
An erratum to this article can be found at 相似文献
15.
16.
17.
Qun-xing Pan 《代数通讯》2013,41(10):3955-3973
Let H be a Hopf algebra and A an H-bimodule algebra. This article investigates homological dimensions and Gorenstein dimensions of L-R smash products A?H. Several well-known results are generalized. Moreover, we explore the stability of Gorenstein projective (flat) precovers and Gorenstein injective preenvelopes between the category of left A-modules and the category of left A?H-modules. 相似文献
18.
Samir Bouchiba 《代数通讯》2013,41(7):2357-2367
This article is concerned with the dimension theory of tensor products of algebras over a field k. In fact, we provide formulas for the Krull and valuative dimension of A? k B when A and B are k-algebras such that the polynomial ring A[n] is an AF-domain for some positive integer n. Also, we compute dim v (A? k B) in the case where A ? B. 相似文献
19.
A finite semigroup S is said to preserve finite generation (resp., presentability) in direct products, provided that, for every infinite semigroup T, the direct product S × T is finitely generated (resp., finitely presented) if and only if T is finitely generated (resp., finitely presented). The main result of this paper is a constructive necessary and sufficient condition for S to preserve both finite generation and presentability in direct products. The condition is that certain graphs, (s), one for each s S, are all connected. The main result is illustrated in three examples, one of which exhibits a 4-element semigroup that preserves finite generation but not finite presentability in direct products.1991 Mathematics Subject Classification: 20M05, 05C25The first author is financially supported by the Sub-Programa Ciência e Tecnologia do 2° Quadro Comunitário de Apoio (grant number BD/ 15623/98). The author also acknowledges the support of the Centro de Álgebra da Universidade de Lisboa and of the Projecto Praxis 2/2.1/MAT/73/94. The second author acknowledges partial financial support from the Nuffield Foundation. 相似文献
20.
It is well known that every compactification of a completely regular space X can be generated, via a Tychonoff-type embedding, by some suitably chosen subset of C1(X). Different subsets may give rise to equivalent compactifications, and we are concerned with the problem of finding all subsets of C1(X) which yield a given compactification αX. The problem is easier if generalized: we say that a subset F of C1(X) “determines” the compactification αX if αX is the smallest compactification to which every element of F extends, and give a simple necessary and sufficient condition for F to determine a given compactification αX. A number of sufficient conditions for two sets to determine the same compactification are given, and the relation between sets which determine αX and those which generate αX (via an embedding) is considered. Generally, a much smaller set of functions is required to determine αX than to generate it; the number needed to determine αX is never more than the weight of αX?X, while the number required to generate it is, if infinite, equal to the weight of αX. 相似文献