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A representation of a C^*-algebra A is a pair (H,phi) where H is a Hilbert space and phi:A->B(H) is a *-homomorphism. (H,phi) is said to be faithful if phi is injective. For ...

A group action of a topological group G on a topological space X is said to be a proper group action if the mapping G×X->X×X(g,x)|->(gx,x) is a proper map, i.e., inverses of ...

An l_x table is a tabulation of numbers which is used to calculate life expectancies. x n_x d_x l_x q_x L_x T_x e_x 0 1000 200 1.00 0.20 0.90 2.70 2.70 1 800 100 0.80 0.12 ...

A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

Let G=SL(n,C). If lambda in Z^n is the highest weight of an irreducible holomorphic representation V of G, (i.e., lambda is a dominant integral weight), then the G-map ...

A section of a fiber bundle gives an element of the fiber over every point in B. Usually it is described as a map s:B->E such that pi degreess is the identity on B. A ...

A smooth map f:S^1->R^3 whose image has singularities. In particular, in the theory of Vassiliev's knot invariants, singular knots with a finite number of ordinary double ...

A Z-action or N-action. A cascade and a single map X->X are essentially the same, but the term "cascade" is preferred by many Russian authors.

The product of three translations along the directed sides of a triangle through twice the lengths of these sides is the identity map.

One of the Eilenberg-Steenrod axioms which states that, if X is a space with subspaces A and U such that the set closure of A is contained in the interior of U, then the ...