hedgehog space

For any cardinal numberMathworldPlanetmath K, we can form a topological spaceMathworldPlanetmath, called the K-hedgehog space, consisting of the disjoint unionMathworldPlanetmath 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 normalityPlanetmathPlanetmath and compactness properties.


  • 1 L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
Title hedgehog space
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