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dogbone space
In geometric topology, the dogbone space, constructed by , is a quotient space of three-dimensional Euclidean space R3 such that all inverse images of points are points or tame arcs, yet it is not homeomorphic to R3. 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 R1 is homeomorphic to R4.
Although the dogbone space is not a manifold, it is a generalized homological manifold and a homotopy manifold.
==See also==
*Whitehead manifold, a 3-manifold not homeomorphic to R3 whose product with R1 is homeomorphic to R4.
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