Английская Википедия:Dogbone space

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Файл:Bing's Dogbone.tiff
The first stage of the dogbone space construction.

In geometric topology, the dogbone space, constructed by Шаблон:Harvs, is a quotient space of three-dimensional Euclidean space <math>\R^3</math> such that all inverse images of points are points or tame arcs, yet it is not homeomorphic to <math>\R^3</math>. 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. Шаблон:Harvtxt showed that the product of the dogbone space with <math>\R^1</math> is homeomorphic to <math>\R^4</math>.

Although the dogbone space is not a manifold, it is a generalized homological manifold and a homotopy manifold.

See also

References