*Definition [#i1636e61]
-A Hausdorff space X is called preparacompact if each open cover of X has an open refinement &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cmathcal%7bH%7d=%5c%7bH_%7b%5calpha%7d%20:%20%5calpha%5cin%20A%5c%7d%20%5c%5d%7d%25.png);  such that if &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20B%5csubset%20A%20%5c%5d%7d%25.png); is infinite and if &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20p_%7b%5cbeta%7d%5cin%20H_%7b%5cbeta%7d%20%5c%5d%7d%25.png); and &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20q_%7b%5cbeta%7d%5cin%20H_%7b%5cbeta%7d%20%5c%5d%7d%25.png); for each &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cbeta%5cin%20B%20%5c%5d%7d%25.png); with &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20p_%7b%5calpha%7d%5cneq%20p_%7b%5cbeta%7d%20%5c%5d%7d%25.png); and &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20q_%7b%5calpha%7d%5cneq%20q_%7b%5cbeta%7d%20%5c%5d%7d%25.png); for &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5calpha%5cneq%5cbeta%20%5c%5d%7d%25.png); , then the set &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cmathcal%7bQ%7d=%5c%7bq_%7b%5cbeta%7d:%20%5cbeta%5cin%20B%5c%7d%20%5c%5d%7d%25.png); has a limit point iff the set &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cmathcal%7bP%7d=%5c%7bp_%7b%5cbeta%7d:%20%5cbeta%5cin%20B%5c%7d%20%5c%5d%7d%25.png); has a limit point.

*Reference [#l7780234]
-Davis, S.W. and Smith, J.C.,  ''The paracompactness of preparacompact spaces.'', Topology, Proc. Conf., Vol. 4, No.2, Ohio Univ. 1979, 345-360 (1980).