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In geometric topology, the dogbone space, constructed by R. H. Bing, is a quotient space of three-dimensional Euclidean space such that all inverse images of points are points or , 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 and a .
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