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- Dunce_hat_(topology) abstract "In topology, the dunce hat is a compact topological space formed by taking a solid triangle and gluing all three sides together, with the orientation of one side reversed. Simply gluing two sides oriented in the same direction would yield a cone much like the layman's dunce cap, but the gluing of the third side results in identifying the base of the cap with a line joining the base to the point. The dunce hat is contractible, but not collapsible. Contractibility can be easily seen by noting that the dunce hat embeds in the 3-ball and the 3-ball deformation retracts onto the dunce hat. Alternatively, note that the dunce hat is the CW-complex obtained by gluing the boundary of a 2-cell onto the circle. The gluing map is homotopic to the identity map on the circle and so the complex is homotopy equivalent to the disc. By contrast, it is not collapsible because it does not have a free face.The name is due to E. C. Zeeman, who observed that any contractible 2-complex (such as the dunce hat) after taking the Cartesian product with the closed unit interval seemed to be collapsible. This observation became known as the Zeeman conjecture and was shown by Zeeman to imply the Poincaré conjecture.".
- Dunce_hat_(topology) thumbnail DunceHatSpace.png?width=300.
- Dunce_hat_(topology) wikiPageID "5148246".
- Dunce_hat_(topology) wikiPageLength "1899".
- Dunce_hat_(topology) wikiPageOutDegree "17".
- Dunce_hat_(topology) wikiPageRevisionID "661152541".
- Dunce_hat_(topology) wikiPageWikiLink CW-complex.
- Dunce_hat_(topology) wikiPageWikiLink CW_complex.
- Dunce_hat_(topology) wikiPageWikiLink Category:Algebraic_topology.
- Dunce_hat_(topology) wikiPageWikiLink Category:Topological_spaces.
- Dunce_hat_(topology) wikiPageWikiLink Christopher_Zeeman.
- Dunce_hat_(topology) wikiPageWikiLink Collapse_(topology).
- Dunce_hat_(topology) wikiPageWikiLink Compact_space.
- Dunce_hat_(topology) wikiPageWikiLink Contractible_space.
- Dunce_hat_(topology) wikiPageWikiLink E._C._Zeeman.
- Dunce_hat_(topology) wikiPageWikiLink Free_face.
- Dunce_hat_(topology) wikiPageWikiLink House_with_two_rooms.
- Dunce_hat_(topology) wikiPageWikiLink Piecewise-linear_collapse.
- Dunce_hat_(topology) wikiPageWikiLink Poincaré_conjecture.
- Dunce_hat_(topology) wikiPageWikiLink Quotient_space_(topology).
- Dunce_hat_(topology) wikiPageWikiLink Topological_space.
- Dunce_hat_(topology) wikiPageWikiLink Topology.
- Dunce_hat_(topology) wikiPageWikiLink Triangle.
- Dunce_hat_(topology) wikiPageWikiLink Zeeman_conjecture.
- Dunce_hat_(topology) wikiPageWikiLink File:DunceHatSpace.png.
- Dunce_hat_(topology) wikiPageWikiLink File:Dunce_hat_animated.gif.
- Dunce_hat_(topology) wikiPageWikiLinkText "Dunce hat (topology)".
- Dunce_hat_(topology) wikiPageWikiLinkText "Dunce hat".
- Dunce_hat_(topology) wikiPageWikiLinkText "dunce cap".
- Dunce_hat_(topology) wikiPageWikiLinkText "dunce hat".
- Dunce_hat_(topology) hasPhotoCollection Dunce_hat_(topology).
- Dunce_hat_(topology) subject Category:Algebraic_topology.
- Dunce_hat_(topology) subject Category:Topological_spaces.
- Dunce_hat_(topology) hypernym Space.
- Dunce_hat_(topology) comment "In topology, the dunce hat is a compact topological space formed by taking a solid triangle and gluing all three sides together, with the orientation of one side reversed. Simply gluing two sides oriented in the same direction would yield a cone much like the layman's dunce cap, but the gluing of the third side results in identifying the base of the cap with a line joining the base to the point. The dunce hat is contractible, but not collapsible.".
- Dunce_hat_(topology) label "Dunce hat (topology)".
- Dunce_hat_(topology) sameAs m.0d4_sw.
- Dunce_hat_(topology) sameAs Шутовской_колпак.
- Dunce_hat_(topology) sameAs Q5314691.
- Dunce_hat_(topology) sameAs Q5314691.
- Dunce_hat_(topology) wasDerivedFrom Dunce_hat_(topology)?oldid=661152541.
- Dunce_hat_(topology) depiction DunceHatSpace.png.
- Dunce_hat_(topology) isPrimaryTopicOf Dunce_hat_(topology).