Dogbone space explained

\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. 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}