House with two rooms: Difference between revisions
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{{Short description|Topological space}} |
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In the [[mathematics|mathematical]] field of [[topology]], '''The House with Two Rooms''' is a particular [[contractible]] [[simplicial complex|2-complex]] that is not [[PL collapse|collapsible]]. |
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[[File:Bing's house.stl|thumb|A 3D model of Bing's house]] |
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[[File:Bing's house with walls removed.stl|thumb|3D model of Bing's house with front and rear walls removed]] |
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'''House with two rooms''' or '''Bing's house''' is a particular [[contractible]], 2-dimensional [[simplicial complex]] that is not [[collapse (topology)|collapsible]]. The name was given by [[R. H. Bing]].<ref>Bing, R. H., ''Some Aspects of the Topology of 3-Manifolds Related to the Poincaré Conjecture'', Lectures on Modern Mathematics, Volume 2, 1964</ref> |
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The house is made of 2-dimensional panels, and has two rooms. The upper room may be entered from the bottom face, while the lower room may be entered from the upper face. There are two small panels attached to the tunnels between the rooms, which make this simplicial complex contractible. |
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The name was given by [[RH Bing]]. |
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== See also == |
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* [[Dogbone space]] |
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* [[Dunce hat (topology)| Dunce hat]] |
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* [[List of topologies]] |
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==External links== |
==External links== |
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*[http://infoshako.sk.tsukuba.ac.jp/~hachi/math/library/bing_eng.html Bing's house with two rooms at Info Shako] |
*[http://infoshako.sk.tsukuba.ac.jp/~hachi/math/library/bing_eng.html Bing's house with two rooms at Info Shako] |
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*[https://ggbm.at/NQfGDDEH A 3D model of Bing's house] - the model can be visualized by using [[Anaglyph 3D|anaglyph glasses]] |
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*[http://mathworld.wolfram.com/Contractible.html Contractible at MathWorld] |
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*[https://www.thingiverse.com/thing:5411507 A printable 3D model] of Bing's house at [[Thingiverse|Thingverse]] |
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== References == |
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{{reflist}} |
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[[Category: |
[[Category:Algebraic topology]] |
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[[Category: |
[[Category:Low-dimensional topology]] |
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Latest revision as of 05:33, 8 May 2024
House with two rooms or Bing's house is a particular contractible, 2-dimensional simplicial complex that is not collapsible. The name was given by R. H. Bing.[1]
The house is made of 2-dimensional panels, and has two rooms. The upper room may be entered from the bottom face, while the lower room may be entered from the upper face. There are two small panels attached to the tunnels between the rooms, which make this simplicial complex contractible.
See also
[edit]External links
[edit]- Bing's house with two rooms at Info Shako
- A 3D model of Bing's house - the model can be visualized by using anaglyph glasses
- A printable 3D model of Bing's house at Thingverse
References
[edit]- ^ Bing, R. H., Some Aspects of the Topology of 3-Manifolds Related to the Poincaré Conjecture, Lectures on Modern Mathematics, Volume 2, 1964
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