Search Results for ""

Let X be a set and S a collection of subsets of X. A subset A subset X is shattered by S if each subset B subset A of A can be expressed as the intersection of A with a ...

A subset E of a topological space S is said to be of first category in S if E can be written as the countable union of subsets which are nowhere dense in S, i.e., if E is ...

A subset E of a topological space S is said to be of second category in S if E cannot be written as the countable union of subsets which are nowhere dense in S, i.e., if ...

A refinement X of a cover Y is a cover such that every element x in X is a subset of an element y in Y.

Let a patch be given by the map x:U->R^n, where U is an open subset of R^2, or more generally by x:A->R^n, where A is any subset of R^2. Then x(U) (or more generally, x(A)) ...

A relation is any subset of a Cartesian product. For instance, a subset of A×B, called a "binary relation from A to B," is a collection of ordered pairs (a,b) with first ...

Let S be the set of all possibilities that satisfy hypothesis H, and let S^' be the set of all possibilities that satisfy hypothesis H^'. Then H^' is a nested hypothesis ...

A subset S subset R^n is said to be pseudo-convex at a point x in S if the associated pseudo-tangent cone P_S(x) to S at x contains S-{x}, i.e., if S-{x} subset P_S(x). Any ...

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.