Dogbone space

In geometric topology, the dogbone space, constructed by , 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. 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.