Simple set: Difference between revisions

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→‎Formal definitions and some properties: hyperimmune and hypersimple
 
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{{expert-subject|1=Mathematics|date=October 2013}}
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The '''three-dimensional torus''', or '''triple torus''', is defined as the [[Cartesian product]] of three circles,
 
:<math>\mathbb{T}^3 = S^1 \times S^1 \times S^1.</math>
 
In contrast, the usual torus is the Cartesian product of two circles only.
 
The triple torus is a three-dimensional [[compact space|compact]] [[manifold]] with no [[manifold#Manifold with boundary|boundary]]. It can be obtained by gluing the three pairs of opposite faces of a [[cube]]. (After gluing the first pair of opposite faces the cube looks like a thick [[Washer (hardware)|washer]], after gluing the second pair &mdash; the flat faces of the washer &mdash; it looks like a hollow torus, the last gluing &mdash; the inner surface of the hollow torus to the outer surface &mdash; is physically impossible in three-dimensional space so it has to happen in four dimensions.)
 
[[Category:Topology]]
[[Category:Differential topology]]
[[Category:Differential geometry]]
[[Category:Geometric topology]]
[[Category:Manifolds]]
 
{{topology-stub}}

Latest revision as of 23:31, 17 April 2014

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