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Locales treated mostly in covariant way

Publication at Faculty of Mathematics and Physics |
2008

Abstract

In particular when dealing with sublocales (but also in other matters) it turns out that it is of advantage to work in the category of locales in a covariant way. Subobjects can be represented as a sort of one-sided ideals with respect to the Heyting operation.

The structure of the lattice (co-frame) of sublocales is now much more transparent. Proofs are much simpler.

Separation, in particular fitness and subfitness, can be now seen in a new perspective.