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.