Summary: It is shown that the locally finite topology \(e^ \tau\) on the hyperspace \(2^ X\) coincides with the topology transmitted by the locally finite covering quasiuniformity on \(X\). We also prove that the following conditions are equivalent: (1) \((X,\tau)\) is paracompact, (2) \((X,\tau)\) is orthocompact and \(e^ \tau= | 2^{u_{FT}}|\), (3) \(e^ \tau=| 2^{u_ L}|\) for some Lebesgue quasiuniformity \(u_ L\). A characterization of feebly compact topological spaces is given.