In
geometric topology
In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, maps between them, particularly embeddings of one manifold into another.
History
Geometric topology as an area distinct from algebraic topo ...
, a branch of mathematics, a crumpled cube is any space in
R3 homeomorphic
In mathematics and more specifically in topology, a homeomorphism ( from Greek roots meaning "similar shape", named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function betw ...
to a
2-sphere
A sphere (from Greek , ) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the ''center' ...
together with its
interior.
[ ] Lininger showed in 1965 that the
union of a crumpled cube and an
open 3-ball glued along their
boundaries is a 3-sphere.
[ ]
References
Geometric topology
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