In this paper, it is shown that the locally finite topology eτ 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 eτ=|2uFT|, ( 3 ) eτ=|2uL| for some Lebesgue quasiuniformity uL·A characterization of feebly compact topological spaces is given. |