GIOVANNI SAMBIN and SILVIO VALENTINI Department of Mathematics, Universitá di Padova Formal Topology aims at the development of topology in a strictly
constructive foundational theory, such as Martin-Lof's constructive
type theory. Its general motivation is to bridge the gap between
ordinary mathematics and computer languages. Type theory is itself
a functional programming language. A toolbox on top of type theory
is provided, which allows ordinary set-theoretic notation. The
main definitions of topology are then expressed in such framework,
which leads to the pointfree approach to topology in a natural
way. The result is formal topology, which then is somehow similar
to the present (impredicative) theory of locales. Its specific
peculiarity is inductive definitions. The generality of definitions
brings to several applications. Temptative contents of 10 ninety-minute lectures:

**Logic**
**F**ORMAL **T**OPOLOGY
**Advanced course**
**Both weeks**
sambin@math.unipd.it and silvio@math.unipd.it
**Course description**

**Prerequisites**
No prerequisite is strictly necessary for the main course, but
obviously the lectures will be more fruitful for students aware
of a little of topology (only the main definitions), type theory,
inductive definitions, locale theory. For specific applications,
something is assumed to be known, on representation of distributive
lattices, sequent calculus, linear logic, etc.
**Literature**
No specific recommendation