House with two rooms or Bing's house is a particular
contractible
In mathematics, a topological space ''X'' is contractible if the identity map on ''X'' is null-homotopic, i.e. if it is homotopic to some constant map. Intuitively, a contractible space is one that can be continuously shrunk to a point within th ...
, 2-dimensional
simplicial complex that is not
collapsible. The name was given by
R. H. Bing.
[Bing, R. H., ''Some Aspects of the Topology of 3-Manifolds Related to the Poincaré Conjecture'', Lectures on Modern Mathematics, Volume 2, 1964]
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
*
Dogbone space
In geometric topology, the dogbone space, constructed by , is a quotient space of three-dimensional Euclidean space \R^3 such that all inverse images of points are points or tame arcs, yet it is not homeomorphic to \R^3. The name "dogbone spac ...
*
Dunce hat
*
List of topologies
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, ...
External links
Bing's house with two rooms at Info ShakoA 3D model of Bing's house
- the model can be visualized by using anaglyph glasses
Anaglyph (Greek ''ana''+''gluphein'' - "to carve") may refer to:
* Anaglyph 3D
Anaglyph 3D is the stereoscopic 3D effect achieved by means of encoding each eye's image using filters of different (usually chromatically opposite) colors, typi ...
A printable 3D model
of Bing's house at Thingverse
References
Low-dimensional topology
{{topology-stub