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The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

A cross-handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in the ...

A special case of Stokes' theorem in which F is a vector field and M is an oriented, compact embedded 2-manifold with boundary in R^3, and a generalization of Green's theorem ...

A set A in a first-countable space is dense in B if B=A union L, where L is the set of limit points of A. For example, the rational numbers are dense in the reals. In ...

A disk algebra is an algebra of functions which are analytic on the open unit disk in C and continuous up to the boundary. A representative measure for a point x in the ...

Two metrics g_1 and g_2 defined on a space X are called equivalent if they induce the same metric topology on X. This is the case iff, for every point x_0 of X, every ball ...

A functor is said to be faithful if it is injective on maps. This does not necessarily imply injectivity on objects. For example, the forgetful functor from the category of ...

If the sampling of an interferogram is modulated at a definite frequency instead of being uniformly sampled, spurious spectral features called "ghosts" are produced (Brault ...

A Hajós group is a group for which all factorizations of the form (say) Z_n=A direct sum B have A or B periodic, where the period is a divisor of n. Hajós groups arose after ...

A family of operators mapping each space M_k of modular forms onto itself. For a fixed integer k and any positive integer n, the Hecke operator T_n is defined on the set M_k ...