Simple set - Revision history

159.83.54.2: /* Formal definitions and some properties */ +iff -> if

2014-04-17T21:31:39Z

Formal definitions and some properties: +iff -> if

← Older revision		Revision as of 23:31, 17 April 2014
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	~~{{expert-subject\|1=Mathematics\|date=October 2013}}~~
	~~{{unreferenced\|date=October 2013}}~~
	}}
	~~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 — the flat faces of the washer — it looks like a hollow torus, the last gluing — the inner surface of the hollow torus to the outer surface — 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}}~~

Deltahedron: /* Formal definitions and some properties */ hyperimmune and hypersimple

2013-04-14T19:03:11Z

Formal definitions and some properties: hyperimmune and hypersimple

← Older revision		Revision as of 21:03, 14 April 2013
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	~~Hello~~, ~~my title is Andrew and my spouse doesn~~'~~t like it at all. For a while I~~'~~ve been in Mississippi but now I~~'~~m contemplating other choices. Office supervising is exactly where her primary income arrives from but she~~'~~s already utilized for an additional one. To climb~~ is ~~some thing I really enjoy performing.~~<br><br>~~My web-site~~ - [~~http://Koreanyelp~~.~~com/index~~.~~php?document_srl=1798~~&~~mid=SchoolNews online psychic readings~~]		{{multiple issues\|
			{{expert-subject\|1=Mathematics\|date=October 2013}}
			{{unreferenced\|date=October 2013}}
			}}
			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 — the flat faces of the washer — it looks like a hollow torus, the last gluing — the inner surface of the hollow torus to the outer surface — 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}}

178.208.131.82: Fixed the definition. Clearly the definition given would include N itself.

2012-02-28T11:06:08Z

Fixed the definition. Clearly the definition given would include N itself.

New page

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