# TOPOLOGY

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