论文标题
前本群的某些特性
Some properties of Pre-topological groups
论文作者
论文摘要
在本文中，我们构成了前本群体的概念和前主管前群体的一些概括。首先，我们系统地研究了前主管群的一些基本特性。特别是，我们证明每个$ t_ {0} $ prepological群体都是规则的，并且每个几乎拓扑组是完全规则的，它扩展了A.A.马尔可夫定理几乎是拓扑组。此外，只有在且只有可以将其嵌入几乎小于或等于$τ$的几乎拓扑群的前期产品的亚组时，就表明它几乎是$τ$ -NARROW。最后，在本阶段的群体类别中研究了基本不变性，预采用性和分解性。
In this paper, we pose the concepts of pre-topological groups and some generalizations of pre-topological groups. First, we systematically investigate some basic properties of pre-topological groups; in particular, we prove that each $T_{0}$ pre-topological group is regular and every almost topological group is completely regular which extends A.A. Markov's theorem to the class of almost topological groups. Moreover, it is shown that an almost topological group is $τ$-narrow if and only if it can be embedded as a subgroup of a pre-topological product of almost topological groups of weight less than or equal to $τ$. Finally, the cardinal invariant, the precompactness and the resolvability are investigated in the class of pre-topological groups.
