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The space of continuously differentiable functions is denoted C^1, and corresponds to the k=1 case of a C-k function.

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

An embedding is a representation of a topological object, manifold, graph, field, etc. in a certain space in such a way that its connectivity or algebraic properties are ...

A bounded operator U on a Hilbert space H is called essentially unitary if U^*U-I and UU^*-I are compact operators.

A fiber space, depending on context, means either a fiber bundle or a fibration.

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.

A property of a space which is also true of each of its subspaces. Being "first-countable" is hereditary, but having a given genus is not.

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

An integral of motion which restricts the phase space available to a dynamical system.