"new foundations must give new math"

from "The Basic Picture. Structures for constructive topology"

by Giovanni Sambin, Oxford University Press, forthcoming


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Under the patronage of

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).

Abstracts » Benini

Marco Benini

Formal Connected Basic Pairs

In this talk, we want to analyze the notion of connected space and connected subset from a constructive point of view in the framework of the Basic Picture.

It will be shown that the Basic Picture allows to give a point-free definition of connected space that is more general than the classical one, although retaining the same intuitive meaning.

Moreover, we will show that there is a close relation between the notions of connection and subspace, and the former allows to derive a sound definition of the latter, based on the 'forget-restore' principle.