منابع مشابه
Coverings of Abelian groups and vector spaces
We study the question how many subgroups, cosets or subspaces are needed to cover a finite Abelian group or a vector space if we have some natural restrictions on the structure of the covering system. For example we determine, how many cosets we need, if we want to cover all but one element of an Abelian group. This result is a group theoretical extension of the theorem of Brouwer, Jamison and ...
متن کاملDual Vector Spaces and Scalar Products
Remember that any linear map is fully determined by its action on an (arbitrary) basis. In fact, for ~v = ∑ 1≤k≤n λk~vk one gets νi(~v) = λi ∈ R (i = 1, . . . , n). We prove that ν1, . . . , νn ∈ V ∗ are linearly independent. Assume that the vector α := ∑ 1≤k≤n μkνk ∈ V ∗ is the zero map. I.e. ν(~v) = 0 ∈ R holds for all ~v ∈ V . Since this holds for all ~v ∈ V , it follows that μ1 = μ2 = · · ·...
متن کاملCrossed Products by Dual Coactions of Groups and Homogeneous Spaces
Mansfield showed how to induce representations of crossed products of C∗algebras by coactions from crossed products by quotient groups and proved an imprimitivity theorem characterising these induced representations. We give an alternative construction of his bimodule in the case of dual coactions, based on the symmetric imprimitivity theorem of the third author; this provides a more workable w...
متن کاملVector Bundles over Classifying Spaces of Compact Lie Groups
The completion theorem of Atiyah and Segal [AS] says that the complex K-theory group K(BG) of the classifying space of any compact Lie group G is isomorphic to R(G)̂ : the representation ring completed with respect to its augmentation ideal. However, the group K(BG) = [BG,Z × BU ] does not directly contain information about vector bundles over the infinite dimensional complex BG itself. The purp...
متن کاملs-Topological vector spaces
In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1968
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1968.26.193