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Sulle topologie compatibili con una data algebra

Maurizio Fattorosi-Barnaba — 1976

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

We call a topology T on a set A compatible with a given algebra 𝒰 = ⟨ A ; F ⟩ 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...

Equivalenze naturali di topologie e semireticoli

Maurizio Fattorosi-Barnaba — 1978

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Some simple results are discussed, connected with another study performed by the Author elsewhere (see references) about the compatibility between a topology and an algebra. In particular, algebraic properties of natural equivalences of topologies are examined, from the point of view of the theory of semilattices.

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