hedgehog space
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.
References
- 1 L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
Title | hedgehog space |
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Canonical name | HedgehogSpace |
Date of creation | 2013-03-22 14:50:02 |
Last modified on | 2013-03-22 14:50:02 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 10 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 54G20 |