Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbau...Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.展开更多
A full characterization is given, in terms of the resolvent R(λ; A) of the infinitesimal generator A of a C0 semigroup T(t) on a Hilbert spaced which assures the continuity for t > t0 (t0 0) of T(t) in the uniform...A full characterization is given, in terms of the resolvent R(λ; A) of the infinitesimal generator A of a C0 semigroup T(t) on a Hilbert spaced which assures the continuity for t > t0 (t0 0) of T(t) in the uniform operator topology.展开更多
In this paper, we show that every weakly a uniform topology （weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short） with which E is a first-countable, zero-dimensional, disconnect...In this paper, we show that every weakly a uniform topology （weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short） with which E is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation ＋ of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation - of effect algebras and the operations A and V of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.展开更多
基金This project partially supported by National Natural Science Foundation of ChinaThis work was partially supported by NSERC of Canada under grant A-8096
文摘Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.
文摘A full characterization is given, in terms of the resolvent R(λ; A) of the infinitesimal generator A of a C0 semigroup T(t) on a Hilbert spaced which assures the continuity for t > t0 (t0 0) of T(t) in the uniform operator topology.
基金Supported by National Natural Science Foundation of China(Grant Nos.11401469 and 11171200)Shaanxi Province Natural Science Foundation(Grant No.2014JQ1032)
文摘In this paper, we show that every weakly a uniform topology （weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short） with which E is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation ＋ of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation - of effect algebras and the operations A and V of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.
