Fattorosi-Barnaba, Maurizio:
Sulle topologie compatibili con una data algebra
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 60 (1976), fasc. n.3, p. 228-234, (Italian)
pdf (561 Kb), djvu (733 Kb). | MR 0460523 | Zbl 0362.54005
Sunto
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.
Referenze Bibliografiche
[1] N. BOURBAKI (1971) - Topologie générale, Hermann, 1971.
[3]
P. M. COHN (
1965) -
Universal algebra,
Harper and Row, Trad, it.:
Feltrinelli,
1971. |
MR 175948[4]
M. FATTOROSI-BARNABA (
1973) -
Elementi di algebra universale,
Bizzarri. |
Zbl 0272.08009[5]
M. FATTOROSI-BARNABA e
L. MAMONE -
Alcune questioni reticolari concernenti certe classi di topologie (in preparazione). |
Zbl 0383.54005[6] G. GRÄTZER (1968) - Universal algebra, D. van Nostrand Co..
[9]
L. S. PONTRJAGIN (
1939) -
Topological groups, trad, ingl.,
Princeton University Press. |
MR 265