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The curvature and torsion functions along a space curve determine it up to an orientation-preserving isometry.

Any collineation from P(V) to P(V), where V is a three-dimensional vector space, is associated with a semilinear map from V to V.

The homeomorphism group of a topological space X is the set of all homeomorphisms f:X->X, which forms a group by composition.

A family of subsets of a topological space such that every point has a neighborhood which intersects only a finite number of them.

A space X is locally pathwise-connected if for every neighborhood around every point in X, there is a smaller, pathwise-connected neighborhood.

An infinite-dimensional differential calculus on the Wiener space, also called stochastic calculus of variations.

The exploration of three-dimensional space from two-dimensional sections of projections of solid bodies.

For any two points x,y in X, there is an open set U such that x in U and y not in U or y in U and x not in U. A space fulfilling this axiom is called a T0-space.

X fulfils the T1-separation axiom and is regular. A space satisfying the T_3-separation axiom is said to be a T3-space.

Maximize the amount of floor space which can be covered with a fixed tile (Hoffman 1998, p. 173).