Hedgehog space
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In mathematics, a hedgehog space is a topological space, consisting of a set of spines joined at a point.
For any cardinal number K, the K-hedgehog space is formed by taking the disjoint union of K real unit intervals identified at the origin. Each unit interval is referred to as one of the hedgehog's spines. A K-hedgehog space is sometimes called a hedgehog space of spininess K.
The hedgehog space is a metric space, when endowed with the hedgehog metric d(x,y) = | x − y | if x and y lie in the same spine, and by d(x,y) = x + y if x and y lie in different spines.
The hedgehog space is an example of a Moore space, and satisfies many strong normality and compactness properties.
[edit] Kowalsky's theorem
Kowalsky's theorem[1] states that any metric space of weight K can be represented as a subspace of the product of countably many K-hedgehog spaces.
[edit] References
- ^ H.J. Kowalsky, Topologische Räume, Birkhäuser, Basel-Stuttgart (1961)
- L.A. Steen, J.A.Seebach, Jr., Counterexamples in Topology, (1970) Holt, Rinehart and Winston, Inc..
- A.V. Arkhangelskii, L.S.Pontryagin, General Topology I, (1990) Springer-Verlag, Berlin. ISBN 3-540-18178-4
- This article incorporates material from Hedgehog space on PlanetMath, which is licensed under the GFDL.
