nLab
annulus

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

Idea

An (open) annulus is a topological space that is homeomorphic to the disk with an interior point removed: D 2{0}D^2 \setminus \{0\}.

An often used model for the corresponding closed annulus is the subspace {(x,y)1x 2+y 24} 2\{(x,y)\mid 1\leq x^2 + y^2 \leq 4\} \subset \mathbb{R}^2, of the plane consisting of the point lying between a unit circle and a circle of radius 2, both centred on the origin.

Revised on November 18, 2014 22:34:09 by Urs Schreiber (217.155.201.6)