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- Dendroid_(topology) abstract "In mathematics, a dendroid is type of topological space, satisfying the properties that it is hereditarily unicoherent (meaning that every subcontinuum of X is unicoherent), arcwise connected, and forms a continuum. The term dendroid was introduced by Bronisław Knaster lecturing at the University of Wrocław, although these spaces were studied earlier by Karol Borsuk and others.Borsuk (1954) proved that dendroids have a fixed-point theorem: every continuous function from a dendroid to itself has a fixed point. Cook (1970) proved that every dendroid is tree-like, meaning that it has arbitrarily fine open covers whose nerve is a tree. The question of whether more generally every tree-like continuum has a fixed-point theorem, posed by Bing (1951) has been solved by David P. BellamyIn Knaster's original publication on dendroids, in 1961, he posed the problem of characterizing the dendroids that can be embedded into the Euclidean plane, which also remains open. Another problem posed in the same year by Knaster, on the existence of an uncountable collection of dendroids with the property that no dendroid in the collection has a continuous surjection onto any other dendroid in the collection, was solved by Minc (2010) and Islas (2007).A locally connected dendroid is called a dendrite. A cone over the Cantor set (called a Cantor fan) is an example of a dendroid that is not a dendrite.".
- Dendroid_(topology) thumbnail Dendrite_julia.png?width=300.
- Dendroid_(topology) wikiPageID "8248350".
- Dendroid_(topology) wikiPageLength "4772".
- Dendroid_(topology) wikiPageOutDegree "17".
- Dendroid_(topology) wikiPageRevisionID "609936905".
- Dendroid_(topology) wikiPageWikiLink Bronisław_Knaster.
- Dendroid_(topology) wikiPageWikiLink Cantor_fan.
- Dendroid_(topology) wikiPageWikiLink Cantor_set.
- Dendroid_(topology) wikiPageWikiLink Category:Continuum_theory.
- Dendroid_(topology) wikiPageWikiLink Category:Trees_(topology).
- Dendroid_(topology) wikiPageWikiLink Connected_space.
- Dendroid_(topology) wikiPageWikiLink Continuum_(topology).
- Dendroid_(topology) wikiPageWikiLink Dendrite_(mathematics).
- Dendroid_(topology) wikiPageWikiLink Euclidean_plane.
- Dendroid_(topology) wikiPageWikiLink Fixed-point_theorem.
- Dendroid_(topology) wikiPageWikiLink Karol_Borsuk.
- Dendroid_(topology) wikiPageWikiLink Nerve_of_a_covering.
- Dendroid_(topology) wikiPageWikiLink Surjection.
- Dendroid_(topology) wikiPageWikiLink Surjective_function.
- Dendroid_(topology) wikiPageWikiLink Topological_space.
- Dendroid_(topology) wikiPageWikiLink Two-dimensional_space.
- Dendroid_(topology) wikiPageWikiLink Unicoherent.
- Dendroid_(topology) wikiPageWikiLink Unicoherent_space.
- Dendroid_(topology) wikiPageWikiLink University_of_Wrocław.
- Dendroid_(topology) wikiPageWikiLink File:Dendrite_julia.png.
- Dendroid_(topology) wikiPageWikiLinkText "Dendroid (topology)".
- Dendroid_(topology) wikiPageWikiLinkText "dendroid".
- Dendroid_(topology) hasPhotoCollection Dendroid_(topology).
- Dendroid_(topology) wikiPageUsesTemplate Template:Harvtxt.
- Dendroid_(topology) wikiPageUsesTemplate Template:Reflist.
- Dendroid_(topology) wikiPageUsesTemplate Template:Topology-stub.
- Dendroid_(topology) subject Category:Continuum_theory.
- Dendroid_(topology) subject Category:Trees_(topology).
- Dendroid_(topology) hypernym Space.
- Dendroid_(topology) comment "In mathematics, a dendroid is type of topological space, satisfying the properties that it is hereditarily unicoherent (meaning that every subcontinuum of X is unicoherent), arcwise connected, and forms a continuum.".
- Dendroid_(topology) label "Dendroid (topology)".
- Dendroid_(topology) sameAs m.026xr1_.
- Dendroid_(topology) sameAs Q5256753.
- Dendroid_(topology) sameAs Q5256753.
- Dendroid_(topology) wasDerivedFrom Dendroid_(topology)?oldid=609936905.
- Dendroid_(topology) depiction Dendrite_julia.png.
- Dendroid_(topology) isPrimaryTopicOf Dendroid_(topology).
