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Given a complex Hilbert space H with associated space L(H) of continuous linear operators from H to itself, the bicommutant M^('') of an arbitrary subset M subset= L(H) is ...

Let X and Y be CW-complexes, and let f:X->Y be a continuous map. Then the cellular approximation theorem states that any such f is homotopic to a cellular map. In fact, if ...

Given a complex Hilbert space H with associated space L(H) of continuous linear operators from H to itself, the commutant M^' of an arbitrary subset M subset= L(H) is the ...

A homeomorphism, also called a continuous transformation, is an equivalence relation and one-to-one correspondence between points in two geometric figures or topological ...

If f(z) is continuous in a region D and satisfies ∮_gammafdz=0 for all closed contours gamma in D, then f(z) is analytic in D. Morera's theorem does not require simple ...

Let A be a non-unital C^*-algebra. There is a unique (up to isomorphism) unital C^*-algebra which contains A as an essential ideal and is maximal in the sense that any other ...

The Theodorus spiral, also known as the Einstein spiral, Pythagorean spiral, square root spiral, or--to contrast it with certain continuous analogs--the discrete spiral of ...

A vector space with a T2-space topology such that the operations of vector addition and scalar multiplication are continuous. The interesting examples are ...

Let A be a C^*-algebra having no unit. Then A^~=A direct sum C as a vector spaces together with 1. (a,lambda)+(b,mu)=(a+b,lambda+mu). 2. mu(a,lambda)=(mua,mulambda). 3. ...

Given a topological vector space X and a neighborhood V of 0 in X, the polar K=K(V) of V is defined to be the set K(V)={Lambda in X^*:|Lambdax|<=1 for every x in V} and where ...