Search Results for ""

A subset of a topological space is called clopen if it is both closed and open.

An extension A subset B of a group, ring, module, field, etc., such that A!=B.

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

A generating function f(x) is a formal power series f(x)=sum_(n=0)^inftya_nx^n (1) whose coefficients give the sequence {a_0,a_1,...}. The Wolfram Language command ...

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 formula for the permanent of a matrix perm(a_(ij))=(-1)^nsum_(s subset= {1,...,n})(-1)^(|s|)product_(i=1)^nsum_(j in s)a_(ij), where the sum is over all subsets of ...

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 ...