共查询到20条相似文献,搜索用时 509 毫秒
1.
For a non-degenerate convex subset Y of the n -dimensional Euclidean space Rn, let F(Y) be the family of all fuzzy sets of Rn which are upper semicontinuous, fuzzy convex and normal with compact supports contained in Y . We show that the space F(Y) with the topology of sendograph metric is homeomorphic to the separable Hilbert space ?2 if Y is compact; and the space F(Rn) is also homeomorphic to ?2. 相似文献
2.
Let F be either the real number field R or the complex number field C and RPn the real projective space of dimension n. Theorems A and C in Hemmi and Kobayashi (2008) [2] give necessary and sufficient conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m?n. In this paper, we simplify the theorems and apply them to the tangent bundle of RPn, its complexification, the normal bundle associated to an immersion of RPn in Rn+r(r>0), and its complexification. Our result for the normal bundle is a generalization of Theorem A in Kobayashi et al. (2000) [8] and that for its complexification is a generalization of Theorem 1 in Kobayashi and Yoshida (2003) [5]. 相似文献
3.
For a simple complex Lie algebra g we study the space of invariants A=(?g?⊗g?)g, which describes the isotypic component of type g in ?g?, as a module over the algebra of invariants (?g?)g. As main result we prove that A is a free module, of rank twice the rank of g, over the exterior algebra generated by all primitive invariants in (?g?)g, with the exception of the one of highest degree. 相似文献
4.
5.
6.
The concept of a relatively weakly injective pair of operator systems is introduced and studied in this paper, motivated by relative weak injectivity in the C*-algebra category. E. Kirchberg [11] proved that the C?-algebra C?(F∞) of the free group F∞ on countably many generators characterises relative weak injectivity for pairs of C?-algebras by means of the maximal tensor product. One of the main results of this paper shows that C?(F∞) also characterises relative weak injectivity in the operator system category. A key tool is the theory of operator system tensor products and . 相似文献
7.
8.
9.
10.
11.
12.
In the present article we provide a sufficient condition for a closed set F∈Rd to have the following property which we call c -removability: Whenever a continuous function f:Rd→R is locally convex on the complement of F , it is convex on the whole Rd. We also prove that no generalized rectangle of positive Lebesgue measure in R2 is c-removable. Our results also answer the following question asked in an article by Jacek Tabor and Józef Tabor (2010) [5]: Assume the closed set F⊂Rd is such that any locally convex function defined on Rd?F has a unique convex extension on Rd. Is F necessarily intervally thin (a notion of smallness of sets defined by their “essential transparency” in every direction)? We prove the answer is negative by finding a counterexample in R2. 相似文献
13.
14.
15.
16.
17.
18.
19.