Dogbone space

File:Bing's Dogbone.tiff

The first stage of the dogbone space construction.

In geometric topology, the dogbone space, constructed by Template:Harvs, is a quotient space of three-dimensional Euclidean space ${ℝ}^3$ such that all inverse images of points are points or tame arcs, yet it is not homeomorphic to ${ℝ}^3$. The name "dogbone space" refers to a fanciful resemblance between some of the diagrams of genus 2 surfaces in R. H. Bing's paper and a dog bone. Template:Harvtxt showed that the product of the dogbone space with ${ℝ}^1$ is homeomorphic to ${ℝ}^4$.

Although the dogbone space is not a manifold, it is a generalized homological manifold and a homotopy manifold.

See also

• List of topologies
• Whitehead manifold, a contractible 3-manifold not homeomorphic to ${ℝ}^3$.

References

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