Description of locally finite families from a nonstandard point of view

In nonstandard topology we can describe a given topology by the neighbourhood-monads of the standard points (see Sari, chapter 6 in Diener and Diener [2]). Calling an internal point near-standard if it is contained in the neighbourhood-monad of some standard point and remote otherwise we give some statements about locally finite families and paracompact spaces in terms of nearstandard and remote points. 2000 Mathematics Subject Classification 03H05 (primary); 54J05 (secondary)