双参数半群拓扑与双连续半群拓扑的研究

发布时间：2018-09-05 05:48

【摘要】：本文根据半群拓扑理论,结合双参数C-半群,双连续n次积分C-半群,双连续α次积分C-半群,完全连续的广义C0-半群以及完全连续的广义C-半群,分别提出了双参数C-半群拓扑,弱双参数C-半群拓扑,双连续n次积分C-半群拓扑,双连续α次积分C-半群拓扑,完全连续的广义C0-半群拓扑及完全连续的广义C-半群拓扑的概念,并对它们的性质及其在新的拓扑意义下的半群性质做了研究.本文主要包括以下几个部分:第一部分,利用双参数C-半群{T(s,t)s,t≥0}的定义,构造了半范数(?),从而分别提出了双参数C-半群拓扑和弱双参数C-半群拓扑的概念,并对它们各自的分离性,完备性,拓扑强弱性进行了研究.第二部分,利用双连续n次积分C-半群{T(t)}t≥0的定义.构造出了半范数(?),x∈X,t≥0,从而引入双连续n次积分C-半群拓扑的概念,并对它的分离性,完备性,拓扑强弱性进行了研究.为了更进一步,结合双连续α次积分C-半群{T(t)}t≥0的定义,构造了半范数(?),x∈X,t≥0,引入了双连续α次积分C-半群拓扑的概念.并对它的分离性,完备性,拓扑强弱性进行了研究.第三部分,利用完全连续的广义C0-半群{T(t)}t≥0定义,构造了半范数(?),x∈X,从而引入了完全连续的广义C0-半群拓扑概念,并对其分离性,完备性,拓扑强弱性进行了研究.为了更进一步,结合完全连续的广义C-半群{T(t)t≥0,构造出了半范数(?),x ∈ X,引入完全连续的广义C-半群拓扑,并对其分离性,完备性,拓扑强弱性进行了研究.
[Abstract]:In this paper, according to the topological theory of semigroup, we combine biparametric C- semigroup, bicontinuous n-degree integral C-semigroup, bicontinuous 伪 -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 伪 degree integral C semigroup topology, the double continuous 伪 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，

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