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The problem of deciding if two knots in three-space are equivalent such that one can be continuously deformed into another.

Given a map f from a space X to a space Y and another map g from a space Z to a space Y, a lift is a map h from X to Z such that gh=f. In other words, a lift of f is a map h ...

A subset M of a Hilbert space H is a linear manifold if it is closed under addition of vectors and scalar multiplication.

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

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

A mathematical structure (e.g., a group, vector space, or smooth manifold) in a category.

One of the eight regions of space defined by the eight possible combinations of signs (+/-,+/-,+/-) for x, y, and z.

The orthogonal complement of a subspace V of the vector space R^n is the set of vectors which are orthogonal to all elements of V. For example, the orthogonal complement of ...

A triple (S,S,P) on the domain S, where (S,S) is a measurable space, S are the measurable subsets of S, and P is a measure on S with P(S)=1.

A metric space Z^^ in which the closure of a congruence class B(j,m) is the corresponding congruence class {x in Z^^|x=j (mod m)}.