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Sulle topologie compatibili con una data algebra

Maurizio Fattorosi-Barnaba

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1976)

  • Volume: 60, Issue: 3, page 228-234
  • ISSN: 0392-7881

Abstract

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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 of a particular case of a compatible topology, whose importance in classical theories (for example, topological groups) is well-known.

How to cite

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Fattorosi-Barnaba, Maurizio. "Sulle topologie compatibili con una data algebra." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 60.3 (1976): 228-234. <http://eudml.org/doc/291057>.

@article{Fattorosi1976,
author = {Fattorosi-Barnaba, Maurizio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {ita},
month = {3},
number = {3},
pages = {228-234},
publisher = {Accademia Nazionale dei Lincei},
title = {Sulle topologie compatibili con una data algebra},
url = {http://eudml.org/doc/291057},
volume = {60},
year = {1976},
}

TY - JOUR
AU - Fattorosi-Barnaba, Maurizio
TI - Sulle topologie compatibili con una data algebra
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1976/3//
PB - Accademia Nazionale dei Lincei
VL - 60
IS - 3
SP - 228
EP - 234
LA - ita
UR - http://eudml.org/doc/291057
ER -

References

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  1. BOURBAKI, N. (1971) - Topologie générale, Hermann, 1971. 
  2. BULMAN-FLEMING, S. (1971) - Congruence topologies on universal algebras, «Math. Z.», 119, 287-289. Zbl0201.02001MR280426DOI10.1007/BF01109881
  3. COHN, P. M. (1965) - Universal algebra, Harper and Row, Trad, it.: Feltrinelli, 1971. MR175948
  4. FATTOROSI-BARNABA, M. (1973) - Elementi di algebra universale, Bizzarri. Zbl0272.08009
  5. FATTOROSI-BARNABA, M. e MAMONE, L. - Alcune questioni reticolari concernenti certe classi di topologie (in preparazione). Zbl0383.54005
  6. GRÄTZER, G. (1968) - Universal algebra, D. van Nostrand Co.. 
  7. HÄMISCH, W. (1954) - Über die Topologie in der Algebra, «Math. Z.», 60, 458-487. Zbl0059.02401MR65142DOI10.1007/BF01187389
  8. HUSAIN, T. (1966) - Introduction to topological groups, W. B. Saunders Co.. Zbl0136.29402MR200383
  9. PONTRJAGIN, L. S. (1939) - Topological groups, trad, ingl., Princeton University Press. MR265

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