The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an a...

The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an a...

Given two quasi-Banach ideals A and B we investigate the regular hull of their composition (A ◦ B). In concrete situations this regular hull appears more often than the composition itself. As a first example we obtain a description for the regular hull of the nuclear operators which is a ”reflected” Grothendieck representation: N reg 1 = I ◦W (theorem 2.1). Further we recognize that the class o...

We prove that certain classes of von Neumann algebras with regular, injective subalgebras are thin. As a consequence, all Hochschild cohomology groups of these algebras are zero. Mathematics subject classification (2010): 46L10, 47A16.

Characterisations of those separable C∗-algebras that have type I injective envelopes or W∗-algebra injective envelopes are presented. An operator system I is injective if for every inclusion E ⊂ F of operator systems each completely positive linear map ω : E → I has a completely positive extension to F . An injective envelope of an operator system E is an injective operator system I such that ...

All weakly distance-regular digraphs with girth $2$ and k-k_{1,1}=1 are classified. A Family of Weakly Distance-Regular Digraphs of Girth 2 Kaishun Wang∗ School of Mathematical Sciences Beijing Normal University Beijing 100875, P.R. China Abstract All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 are classified.All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 ...

In this paper, we give two constructions of weakly distance-regular digraphs of girth 2, and prove that certain quotient digraph of a commutative weakly distancetransitive digraph of girth 2 is a distance-transitive graph. As an application of the result, we not only give some constructions of weakly distance-regular digraphs which are not weakly distance-transitive, but determine a special cla...