nLab
square

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

Geometry

Contents

Idea

As a polygon the square is the regular 4-gon.

As a topological space it is the product topological space of the bounded closed interval with itself, [0,1] 2[0,1]^2 .

Quotients

The identification of opposite sides of the square yields the cylinder and the torus.

And the identification with opposite orientation yields the Möbius strip.

graphics grabbed from Lawson 03

References

  • Terry Lawson, Topology: A Geometric Approach, Oxford University Press (2003) (pdf)

Last revised on April 27, 2017 at 02:25:58. See the history of this page for a list of all contributions to it.