# nLab square

Contents

This entry is about squares in geometry. For squares in category theory see commutative square. For squares in ring theory, see square function. For squares in type theory, see square type.

# 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, $[0,1]^2$ .

## 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 May 12, 2022 at 23:15:28. See the history of this page for a list of all contributions to it.