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Suppose that X^~,X are arcwise-connected and locally arcwise-connected topological spaces. Then (X^~,p) is said to be a covering space of X if p:X^~->X is a surjective ...

The set of all Schwartz functions is called a Schwartz space and is denoted S(R^n). If C_0^infty(R^n) denotes the set of smooth functions of compact support on R^n, then this ...

Teichmüller's theorem asserts the existence and uniqueness of the extremal quasiconformal map between two compact Riemann surfaces of the same genus modulo an equivalence ...

If 0<p<infty, then the Hardy space H^p(D) is the class of functions holomorphic on the disk D and satisfying the growth condition ...

A complete metric space is a metric space in which every Cauchy sequence is convergent. Examples include the real numbers with the usual metric, the complex numbers, ...

A sigma-compact topological space is a topological space that is the union of countably many compact subsets.

The dual vector space to a real vector space V is the vector space of linear functions f:V->R, denoted V^*. In the dual of a complex vector space, the linear functions take ...

According to most authors (e.g., Kelley 1955, p. 113; McCarty 1967, p. 144; Willard 1970, p. 92) a regular space is a topological space in which every neighborhood of a point ...

A metric space X is boundedly compact if all closed bounded subsets of X are compact. Every boundedly compact metric space is complete. (This is a generalization of the ...

A Euclidean-like space having line element ds^2=(dz^1)^2+...+(dz^p)^2-(dz^(p+1))^2-...-(dz^(p+q))^2, having dimension m=p+q (Rosen 1965). In contrast, the signs would be all ...