Study On The Two Parameter Semigroups Topology And The Bi-Continuous Semigroups Topology

According to the theory of semigroup topology,combined with the two parameter C-semigroups,bi-continuous n-times integrated C-semigroups,bi-continuous?-times integrated C-semigroups,completely continuous generalized C0-semigroups and completely continuous generalized C-semigroups,two parameter C-semigroups topology,weak two parameter C-semigroups topology,bi-continuous n-times integrated C-semigroups topology,bi-continuous ?-times integrated C-semigroups topology,completely continuous generalized C0-semigroups topology and completely continuous generalized C-semigroups topology are proposed respectively,and their properties along with properties under the new topological meaning are studied.This paper mainly includes the following parts:The first part,seminorm(?),x?X and seminorm(?),x?X are induced by using two parameter C-semigroups {T(s,t)}s,t?0},the concept of two parameter C-semigroups topology and weak two parameter C-semigroups topology are given,and studied their respective separability,completeness,topological strength.The second part,seminorm(?),x?X,t?O is induced by using bi-continuous n-times integrated C-semigroups {T(s,t)}s,t?0},the concept of bi-continuous n-times integrated C-semigroups topology is given,and studied its separability,completeness,the topological strength.In order to research further,seminorm(?),X?X,t?O is induced by bi-continuous ?-times integrated C-semigroups {T(t)}t?0,the concept of bi-continuous ?-times integrated C-semigroups topology is given,and studied its separability,completeness,the topological topology.The third part,seminorm(?),x?is induced by using completely continuous generalized C0-semigroups {T(t)}t?0,the concept of completely continuous generalized C0-semigroups topology is given,and studied its separability,completeness,the topological topology.In order to research further,seminorm(?),x?X is induced by using completely continuous generalized C-semigroups {T(t)}t?0,the concept of completely continuous generalized C-semigroups topology is given,and studied its separability,completeness,the topological topology.