Nonstandard analysis in topology: Nonstandard and standard compactifications

Let (X, T) he a topological space and *X a nonstandard extension of X. Sets of, the form (*)G. where G epsilon T. form a base for the "standard" topol ogy T-S on X-*. The topological space (*X, T-S) will be used tu study compa ctifications of (X, T) in a systematic way.