Definition:Torus (Topology)/General/Definition 1

Definition

The $n$-dimensional torus (or $n$-torus) $\Bbb T^n$ is defined as the $n$-fold product space of the $1$-sphere.

That is:

$\ds \Bbb T^n = \prod_{i \mathop \in \N_{< n}} \Bbb S^1$

where:

$\Bbb S^1$ denotes the $1$-sphere

$\N_{< n}$ denotes an initial segment of natural numbers

$\ds \prod_{i \mathop \in I}$ denotes the product space

Also see

• Equivalence of Definitions of Torus of Arbitrary Dimension

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