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- Hawaiian_earring abstract "In mathematics, the Hawaiian earring H is the topological space defined by the union of circles in the Euclidean plane R2 with center (1/n, 0) and radius 1/n for n = 1, 2, 3, .... The space H is homeomorphic to the one-point compactification of the union of a countably infinite family of open intervals.The Hawaiian earring can be given a complete metric and it is compact. It is path connected but not semilocally simply connected.The Hawaiian earring looks very similar to the wedge sum of countably infinitely many circles; that is, the rose with infinitely many petals, but those two spaces are not homeomorphic. The difference between their topologies is seen in the fact that, in the Hawaiian earring, every open neighborhood of the point of intersection of the circles contains all but finitely many of the circles. It is also seen in the fact that the wedge sum is not compact: the complement of the distinguished point is a union of open intervals; to those add a small open neighborhood of the distinguished point to get an open cover with no finite subcover.".
- Hawaiian_earring thumbnail Hawaiian_Earrings.svg?width=300.
- Hawaiian_earring wikiPageID "910263".
- Hawaiian_earring wikiPageRevisionID "605015464".
- Hawaiian_earring hasPhotoCollection Hawaiian_earring.
- Hawaiian_earring subject Category:Topological_spaces.
- Hawaiian_earring type Abstraction100002137.
- Hawaiian_earring type Attribute100024264.
- Hawaiian_earring type MathematicalSpace108001685.
- Hawaiian_earring type Set107999699.
- Hawaiian_earring type Space100028651.
- Hawaiian_earring type TopologicalSpaces.
- Hawaiian_earring comment "In mathematics, the Hawaiian earring H is the topological space defined by the union of circles in the Euclidean plane R2 with center (1/n, 0) and radius 1/n for n = 1, 2, 3, .... The space H is homeomorphic to the one-point compactification of the union of a countably infinite family of open intervals.The Hawaiian earring can be given a complete metric and it is compact.".
- Hawaiian_earring label "Hawaiian earring".
- Hawaiian_earring sameAs m.03p1qg.
- Hawaiian_earring sameAs Q5684591.
- Hawaiian_earring sameAs Q5684591.
- Hawaiian_earring sameAs Hawaiian_earring.
- Hawaiian_earring wasDerivedFrom Hawaiian_earring?oldid=605015464.
- Hawaiian_earring depiction Hawaiian_Earrings.svg.
- Hawaiian_earring isPrimaryTopicOf Hawaiian_earring.
