Resumen de On Two Questions About Topological (and Nonstandard) Extensions

Camillo Costantini

• We construct, under MA, a non-Hausdorff (T1-)topological extension *? of ?, such that every function from ? to ? extends uniquely to a continuous function from *? to *?. We also show (in ZFC) that for every nontrivial topological extension *X of a countable set X there exists a topology tf on *X, strictly finer than the Star topology, and such that (*X, tf) is still a topological extension of X with the same function extensions *f. This solves two questions raised by M. Di Nasso and M. Forti.