Pervin spaces and Frith frames: bitopological aspects and completion
 
 
Description: 

A Pervin space is a set equipped with a bounded sublattice of its powerset, while its pointfree version, called Frith frame, consists of a frame equipped with a generating bounded sublattice. It is known that the dual adjunction between topological spaces and frames extends to a dual adjunction between Pervin spaces and Frith frames, and that the latter may be seen as representatives of certain quasi-uniform structures. As so, they have an underlying bitopological structure and inherit a natural notion of completion. In this talk, we will start
by exploring the bitopological nature of Pervin spaces and of Frith frames, proving a couple of categorical equivalences involving zero-dimensional structures. We will then see that the categories of T0 complete Pervin spaces and of complete Frith frames are dually equivalent. This allows us to interpret several Stone-type dualities as a restriction of the dual adjunction between Pervin spaces and Frith frames along full subcategory embeddings.

 

This is based on joint work with Anna Laura Suarez.

 

Date:  2023-01-24
Start Time:   16:00
Speaker:  Célia Borlido (CMUC, Univ. Coimbra)
Institution:  CMUC, University of Coimbra
Place:  Sala 2.4, DMUC
Research Groups: -Algebra, Logic and Topology
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