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.

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