关于具(A_1)公理的拓扑群中集合的紧性(英文)

Compactness in Topological Groups with the Axiom(A_1)

研究了具(A_1)公理的拓扑群中集合的相对紧、全有界和序列紧之间的关系,给出了具(A_1)公理的拓扑群中集合相对紧的充分必要条件为该集合是序列紧的.

The relative compactness of subsets, the total boundedness of subsets and sequential compactness of subsets in topological groups with the axiom（A1） are concerned. The conclusion is obtained that a subset A in topological groups with the axiom （A1） is relatively compact if and only if every sequence of point in A can obtain a convergent subsequence.