Nonstandard analysis in topology: Nonstandard and standard compactifications (Q2710611)

It has been known since the 1970s that certain aspects of nonstandard analysis are in correspondence with ultrafilter spaces. The first author previously investigated a topology on ultrafilter spaces that corresponds to the ``standard'' topology discussed in this paper via nonstandard analysis [Port. Math. 57, No. 4, 481-492 (2000; Zbl 0964.54033)]. In this paper, Robinson styled nonstandard analysis is used and if \((X,T)\) is a topological space, then \(\{{}^* G \mid G \in T\}\) is a base for an S-topology \({}^ST\) on \({}^*T.\) The authors study the space \(({}^*X,{}^ST)\) mostly relative to compactifications and obtain results many of which are similar to those obtained in the above mentioned reference.