"new foundations must give new math"
from "The Basic Picture. Structures for constructive
topology"
by Giovanni Sambin, Oxford University Press, forthcoming
To register send an e-mail to maietti @ math.unipd.it
Registration fee: 40 euros
(to be paid at arrival).
Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Italy
University of Padova, Italy
AILA (Italian Association of Logic and Applications), whose first president was Giovanni Sambin (from 1987 to 1994).
Silvio Valentini
Padova
Relative Formal Topology: ten years later
Ten years ago relative formal topologies have been proposed as a
way to combine a binary positivity predicate with a suitable cover
relation in such a way that they enjoy both monotonicity and positivity.
Now they are a suitable tool to make explicit the relevance of the
binary positivity predicate, to simplify the definition of formal
point and continuous relation and to deal with the topology induced
on closed subsets.
Here we show how to provide a complete formalisation for relative
formal topologies both in an impredicative and a predicative setting,
we propose for them an axiomatic definition and we provide a complete
characterisation of continuous relations which suggests the definition
of a (new?) category of relative formal topologies.