A "one for the price of zero" duality principle for distributive spaces
 
 
Description:  Our study of topological spaces presented as convergence structures shaped the idea
that "topological spaces are generalised orders", and eventually revealed the
following analogies.

down-closed subset                                   = filter of opens
non-empty down-closed subset                  = proper filter of opens
directed down-closed subset                       = prime filter of opens
upper bound                                            = limit point
supremum                                               = smallest limit point
cocomplete ordered set                             = continuous lattice
directed cocomplete ordered set                 = stably compact space
completely distributive lattice                     = ???
continuous directed cocomplete ordered set = ???

In this seminar we try to remove the two remaining question marks. Furthermore, we
show that the category of distributive spaces is dually equivalent to a category of
frames by simply observing that both sides represent the idempotent splitting
completion of the same category.

Date:  2010-11-09
Start Time:   16:30
Speaker:  Dirk Hofmann (U. Aveiro)
Institution:  Universidade de Aveiro
Place:  Sala 5.5
Research Groups: -Algebra, Logic and Topology
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