Definition:Torus (Topology)/General/Definition 2

Definition

The $n$-dimensional torus (or $n$-torus) $\Bbb T^n$ is defined as the space whose points are those of the cross product of $n$ circles:

$\Bbb T^n = \underbrace{\Bbb S^1 \times \Bbb S^1 \times \ldots \times \Bbb S^1}_{n \text{ times}}$

and whose topology $\tau_{\Bbb T^n}$ is generated by the basis:

$\BB = \set {U_1 \times U_2 \times \cdots \times U_n : U_1, U_2, \ldots, U_n \in \tau_{\Bbb S^1}}$

where $\tau_{\Bbb S^1}$ is the topology of the $1$-sphere.

Also see

• Equivalence of Definitions of Torus of Arbitrary Dimension

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.