Dogbone space
Introduction The first stage of the dogbone space construction.In geometric topology, the '''dogbone space''',  constructed by  , 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. showed that the product of the dogbone space with  is homeomorphic to .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 .
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