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*As far as we know, it is an open question whether *X can be To when X is infinite and * is Ol-saturated. However, with the help of extra set theory (notably Martin’s Axiom (MA) and the Continuum Hypothesis (CH)), we can construct extensions * in which *X can be To (even Tichonov) for a large class of spaces X. To begin with, we confine our attention to ultrapower extensions * IIo() where D is a free (that is, nonprincipal) ultrafilter on a countable set I. Then * is automatically e01-saturated (since Dis countably incomplete) and its elements are equivalence classes [f] [f]o of functions f d; [30 {g

Coarse topologies in nonstandard extensions via separative ultrafilters