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Un problema inerente al reticolo delle topologie su di una potenza cartesiana

Luigi F. Mamone — 1977

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

We investigate the lattice structure of the set of box topologies within the lattice of all topologies of a cartesian power for a given set and find out that it is a sub-V-semilattice but not, in general, a sublattice. Further we show that it is a sublattice iff the given set is finite. Starting from these results we remark that the set of all topologies compatible with a given algebra is a complete semilattice but not, in general, a lattice.

Compatibilità ed equivalenze naturali di una topologia

Maurizio Fattorosi-Barnaga;  Luigi F. Mamone — 1977

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

We first extend, in the strongest possible way, a necessary condition for compatibility of a topology with an algebra obtained by the first author in a previous paper [14]: this extension is not yet sufficient for compatibility and so another approach to the characterization problem for compatibility is needed. An attempt in a new direction turns out to be successful but in an excessively general frame: in fact it leads to a new (as far as we know) characterization of continuity of a function between...

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