nLab principle of enough functions

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Analysis

Constructivism, Realizability, Computability

Foundations

foundations

The basis of it all

 Set theory

set theory

Foundational axioms

foundational axioms

Removing axioms

Contents

Idea

The principle of enough functions states that the formal locale of the function space \mathbb{R}^\mathbb{R} of continuous real endofunctions is a spatial locale.

The principle of enough functions is true in classical mathematics, but cannot be proven in neutral constructive mathematics and so has to be added as an axiom.

References

Created on April 14, 2025 at 21:27:45. See the history of this page for a list of all contributions to it.