On Two Questions About Topological (and Nonstandard) Extensions

• Autores: Camillo Costantini
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 148, Nº 3, 2006, págs. 205-216
• Idioma: inglés
• DOI: 10.1007/s00605-006-0384-x
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• Resumen

  • 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.