【摘要】：本文根據(jù)半群拓撲理論,結合雙參數(shù)C-半群,雙連續(xù)n次積分C-半群,雙連續(xù)α次積分C-半群,完全連續(xù)的廣義C0-半群以及完全連續(xù)的廣義C-半群,分別提出了雙參數(shù)C-半群拓撲,弱雙參數(shù)C-半群拓撲,雙連續(xù)n次積分C-半群拓撲,雙連續(xù)α次積分C-半群拓撲,完全連續(xù)的廣義C0-半群拓撲及完全連續(xù)的廣義C-半群拓撲的概念,并對它們的性質(zhì)及其在新的拓撲意義下的半群性質(zhì)做了研究.本文主要包括以下幾個部分:第一部分,利用雙參數(shù)C-半群{T(s,t)s,t≥0}的定義,構造了半范數(shù)(?),從而分別提出了雙參數(shù)C-半群拓撲和弱雙參數(shù)C-半群拓撲的概念,并對它們各自的分離性,完備性,拓撲強弱性進行了研究.第二部分,利用雙連續(xù)n次積分C-半群{T(t)}t≥0的定義.構造出了半范數(shù)(?),x∈X,t≥0,從而引入雙連續(xù)n次積分C-半群拓撲的概念,并對它的分離性,完備性,拓撲強弱性進行了研究.為了更進一步,結合雙連續(xù)α次積分C-半群{T(t)}t≥0的定義,構造了半范數(shù)(?),x∈X,t≥0,引入了雙連續(xù)α次積分C-半群拓撲的概念.并對它的分離性,完備性,拓撲強弱性進行了研究.第三部分,利用完全連續(xù)的廣義C0-半群{T(t)}t≥0定義,構造了半范數(shù)(?),x∈X,從而引入了完全連續(xù)的廣義C0-半群拓撲概念,并對其分離性,完備性,拓撲強弱性進行了研究.為了更進一步,結合完全連續(xù)的廣義C-半群{T(t)t≥0,構造出了半范數(shù)(?),x ∈ X,引入完全連續(xù)的廣義C-半群拓撲,并對其分離性,完備性,拓撲強弱性進行了研究.
[Abstract]:In this paper, according to the topological theory of semigroup, we combine biparametric C- semigroup, bicontinuous n-degree integral C-semigroup, bicontinuous 偽 -integral C-semigroup, completely continuous generalized C0-semigroup and completely continuous generalized C-semigroup. The two parameter C semigroup topology, the weak two parameter C semigroup topology, the double continuous n-degree integral C semigroup topology, the double continuous 偽 degree integral C semigroup topology, the double continuous 偽 degree integral C semigroup topology are presented respectively. The concepts of completely continuous generalized C0-semigroup topology and completely continuous generalized C-semigroup topology are discussed. Their properties and the properties of Semigroups in the new topological sense are studied. This paper mainly includes the following parts: in the first part, by using the definition of two-parameter C- semigroup {T (stt) snt 鈮，

本文編號：2223382