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A subset E of a topological space S is said to be nonmeager if E is of second category in S, i.e., if E cannot be written as the countable union of subsets which are nowhere ...

In a topological space X, an open neighborhood of a point x is an open set containing x. A set containing an open neighborhood is simply called a neighborhood.

A regular surface M subset R^n is called orientable if each tangent space M_p has a complex structure J_p:M_p->M_p such that p->J_p is a continuous function.

Two vectors u and v whose dot product is u·v=0 (i.e., the vectors are perpendicular) are said to be orthogonal. In three-space, three vectors can be mutually perpendicular.

The interval (generally, the smallest interval) over which the values of a periodic function recur. Functions may have one or more periods over time and in space.

Every bounded operator T acting on a Hilbert space H has a decomposition T=U|T|, where |T|=(T^*T)^(1/2) and U is a partial isometry. This decomposition is called polar ...

A polytope in n-dimensional Euclidean space R^n whose vertices are integer lattice points but which does not contain any other lattice points in its interior or on its ...

The two-dimensional space consisting of the set of triples {(a,b,c):a,b,c in K, not all zero}, where triples which are scalar multiples of each other are identified.

The equivalence of manifolds under continuous deformation within the embedding space. Knots of opposite chirality have ambient isotopy, but not regular isotopy.

A retraction is a continuous map of a space onto a subspace leaving each point of the subspace fixed. Alternatively, retraction can refer to withdrawal of a paper containing ...