Sulle topologie compatibili con una data algebra

Fattorosi-Barnaba, Maurizio

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 60 (1976) no. 3, pp. 228-234

Résumé

We call a topology $T$ on a set $A$ compatible with a given algebra $\mathcal{U} = \langle A;F \rangle$ iff all the operations of $F$ are continuous with respect to $T$ in the natural sense. We give a necessary condition for compatibility, we show its insufficiency by a counterexample and we exhibit some examples for which sufficiency holds. Furthermore we make two observations, one consisting in a characterization of the discrete and indiscrete topologies with respect to compatibility, and the other consisting in an algebraic expression of a particular case of a compatible topology, whose importance in classical theories (for example, topological groups) is well-known.