伪-γ空间的若干等价刻画

Some Characterizations of Pseudo-γ Spaces

讨论了一类重要的广义度量空间-伪-γ空间的等价刻画问题,利用o-度量及局部拟一致结构给出对伪-γ空间的若干等价刻画.得到X为伪-γ空间当且仅当存在与X上拓扑相容的具有可数基的局部拟一致结构和X为伪-γ空间当且仅当存在与X上拓扑相容的o-度量d使得对X的任一紧集K及任一闭集F,若K∩F=O,则d(K,F)> 0.

The main purpose of this paper is to discuss the characterization of an important class of generalized metric spaces,i.e.,pseudo-γspaces.We use the notions of o-metrics and local quasi-uniformities to give some characterizations of pseudo-γspaces.The main results are:1.X is a pseudo-γspace if and only if it admits a compatible local quasi-uniformity with a countable base;2.X is a pseudo-γspace if and only if it admits a compatible o-metric d such that for each compact subset K and closed subset F of X,if K∩F=,then d(K,F)>0.