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Let A be a closed convex subset of a Banach space and assume there exists a continuous map T sending A to a countably compact subset T(A) of A. Then T has fixed points.

A subset X subset Y is said to be bicollared in Y if there exists an embedding b:X×[-1,1]->Y such that b(x,0)=x when x in X. The map b or its image is then said to be the ...

The pseudo-tangent cone P_S(x) of a subset S subset R^n at a point x in S is the set P_S(x)=convK_S^_, where K_S is the contingent cone of S and where conv(A) is the smallest ...

A stack F on a topological space X is said to be a stack of groupoids if for each open subset U subset= X, the category F(U) is a groupoid.

A subset M subset R^n is called a regular surface if for each point p in M, there exists a neighborhood V of p in R^n and a map x:U->R^n of an open set U subset R^2 onto V ...

Let S be a nonempty set, then an ultrafilter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F. 2. If A,B in F, then A ...

Let f be a contraction mapping from a closed subset F of a Banach space E into F. Then there exists a unique z in F such that f(z)=z.

Given a set of objects S, a binary relation is a subset of the Cartesian product S tensor S.

A set of class representatives is a subset of X which contains exactly one element from each equivalence class.

An addition chain for which there is a subset H of members such that each member of the chain uses the largest element of H which is less than the member.