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A subset of a topological space which is compact with respect to the relative topology.

A set X is a called a "convex cone" if for any x,y in X and any scalars a>=0 and b>=0, ax+by in X.

If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.

Given a regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the n=5 case of polygon triangle picking, A^_ = ...

A topological space is second countable if it has a countable topological basis.

The closure of a set A is the smallest closed set containing A. Closed sets are closed under arbitrary intersection, so it is also the intersection of all closed sets ...

An array is a "list of lists" with the length of each level of list the same. The size (sometimes called the "shape") of a d-dimensional array is then indicated as ...

The Gaussian integral, also called the probability integral and closely related to the erf function, is the integral of the one-dimensional Gaussian function over ...

An irreducible representation of a group is a group representation that has no nontrivial invariant subspaces. For example, the orthogonal group O(n) has an irreducible ...

The algebraic unknotting number of a knot K in S^3 is defined as the algebraic unknotting number of the S-equivalence class of a Seifert matrix of K. The algebraic unknotting ...