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hedgehog space
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(Definition)
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For any cardinal number $K$ we can form a topological space, called the $K$ hedgehog space, consisting of 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.''
The hedgehog space admits a somewhat surprising metric, by defining $d(x,y)=|x-y|$ 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.
- 1
- L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
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"hedgehog space" is owned by mathcam. [ full author list (2) ]
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Cross-references: properties, compactness, normality, strong, Moore space, metric, origin, intervals, unit, real, disjoint union, topological space, cardinal number
This is version 7 of hedgehog space, born on 2004-11-18, modified 2006-09-06.
Object id is 6500, canonical name is HedgehogSpace.
Accessed 1606 times total.
Classification:
| AMS MSC: | 54G20 (General topology :: Peculiar spaces :: Counterexamples) |
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Pending Errata and Addenda
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