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.

单词	HedgehogSpace
释义	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.
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