Similarly as the sobriety is essential for representing continuous maps as frame homomorphisms, also other separation axioms play a basic role in expressing topological phenomena in frame language. In particular, TD is equivalend with the correctness of viewing subspaces as sublocales, or with representability of open or closed maps as open or closed homomorphisms. A weaker separation axiom is equivalent wth an algebraic recognizability wheter the intersection of a system of open sets remains open or not. The role of sobriety is also being analysed in some detail.

Separation axioms and frame representation of some topological facts

TOZZI, Anna
1994-01-01

Abstract

Similarly as the sobriety is essential for representing continuous maps as frame homomorphisms, also other separation axioms play a basic role in expressing topological phenomena in frame language. In particular, TD is equivalend with the correctness of viewing subspaces as sublocales, or with representability of open or closed maps as open or closed homomorphisms. A weaker separation axiom is equivalent wth an algebraic recognizability wheter the intersection of a system of open sets remains open or not. The role of sobriety is also being analysed in some detail.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/16047
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact