关于某些拟一致空间的超空间拓扑(英文)

On Hyperspace Topologies of Some Quasiuniform Spaces

中文摘要:

      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u_LF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u_L,使e^τ<

英文摘要:

      In this paper, it is shown that the locally finite topology e^τ on the hypers-pace 2^x 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^τ=|2^u_FT|, ( 3 ) e^τ=|2^u_L| for some Lebesgue quasiuniformity u_L·A characterization of feebly compact topological spaces is given.