"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 » Spreen

Dieter Spreen
Siegen

An Intrinsic Characterisation of Effective Topologies

An effective topological space is a two-level structure consisting of two indexed sets: points and basic opens, as well as two enumerable relations between the two levels: membership and convergence.

Numbered sets possess a variety of intrinsic topologies defined by their computability structure.

We characterize those of them that are compatible with the given topology.

As a consequence characterizations for two important types of topologies are obtained.