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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/16047
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