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TOPOLOGY




Moebius Strip II by Escher
Moebius Strip II by M. C. Escher. These ants illustrate the counterintuitive properties of the Möbius band – an ordinary band with a half-twist. All are on the one side but appear to be on opposite sides. A band made with two half-twists does have two sides. The number of twists dictates the number of sides and dramatically affects the result produced by cutting along the middle. Topology allows the exploration and description of such spatial relationships.
   • Alexander's Horned Sphere
   • algebraic topology

   • Banach-Tarski paradox
   • Betti number
   • Borromean rings
   • Borsuk-Ulam theorem
   • braid
   • Brouwer fixed-point theorem
   • bundle

   • Calabi-Yau space
   • closed
   • cohomology
   • connected
   • continuity

   • diffeomorphism
   • differential topology

   • dimension
   • disk (mathematics)

   • Earthshapes
   • Euclidean geometry
   • Euler characteristic

   • foliation

   • genus
   • Gordian Knot

   • hairy ball theorem
   • ham sandwich theorem
   • Hilbert space
   • homeomorphic
   • homology
   • homotopy

   • Klein bottle
   • knot

   • manifold
   • Möbius band

   • non-orientable surface

   • orientable surface

   • pleated surface
   • Poincaré's conjecture
   • point-set topology
   • projective plane

   • Riemann surface
   • round

   • simply-connected
   • space
   • sphere

   • tie knot
   • topological dimension
   • topological group
   • topological space
   • topology
   • torus

   • Whitney's umbrella

Related category

   • SPACE AND TIME


Related supercategory

   • MATHEMATICS