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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 $\mathcal{U}=\langle A;F\rangle$ 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...

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.

Proprietà reticolari di certe classi di topologie

Maurizio Fattorosi-Barnaba; Luigi Mamone — 1976

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

We investigate lattice-theoretical properties concerning certain classes of topologies considered by the first author in a previous paper [2].

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Sulle topologie compatibili con una data algebra

Equivalenze naturali di topologie e semireticoli

Proprietà reticolari di certe classi di topologie