Dogbone space

In geometric topology, the dogbone space, constructed by R. H. Bing (1957), is a quotient space of three-dimensional Euclidean space

such that all inverse images of points are points or tame arcs, yet it is not homeomorphic to

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.

Bing (1959) showed that the product of the dogbone space with

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