nLab Arens-Fort space

Contents

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

Contents

Definition

The Arens-Fort space is the set 2\mathbb{N}^2 of pairs of natural numbers with all subsets not containing (0,0)(0,0) being open and all subsets containing (0,0)(0,0) and containing almost all (all but finitely many) points in almosts all columns being open.

(E.g. Joshi 83, Chapter 4, Section 2, Example 10)

Properties

The Arens-Fort space is:

The Arens-Forst space is not:

References

  • K. D. Joshi: Introduction to General Topology, New Age International (1983) [ISBN 978-0-47027-556-6, gBooks]

See also:

Last revised on June 1, 2024 at 04:15:10. See the history of this page for a list of all contributions to it.