摘要
In this paper, it is shown that the locally finite topology e on the hypers-pace 2X coincides with the topology transmitted by the locally finite covering quasiuniformity on X. We also prove that the following conditions are equiva-lent . (l)(X,τ) is paracompact , (2) (X,τ) is orthcompact ,and e=2Ufr|, ( 3 ) e= \2Ul\ for some Lebesgue quasiuniformity UL . A characterization of feebly compact topological spaces is given.
设(X,τ)是一个拓扑空间。在本文中,我们证明了在超空间2~X上局部有限拓扑e~τ与局部有限覆盖拟一致(?)所导出的超拓扑|2~u_LF|是相同的。我们还证明了下面条件是等价的:(1)(X,τ)是仿紧的;(2)(X,τ)是orth紧的,且e~τ=|2~u_FT|;(3)存在一个Lebes-yue拟一致■,使e~τ=|2~u_L|。同时,我们也给出了feeble—紧拓扑空间的一个特征刻划。
