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One of the Eilenberg-Steenrod axioms. It states that, for every pair (X,A), there is a natural long exact sequence ...->H_n(A)->H_n(X)->H_n(X,A)->H_(n-1)(A)->..., where the ...

The topology induced by a topological space X on a subset S. The open sets of S are the intersections S intersection U, where U is an open set of X. For example, in the ...

Let S be a collection of subsets of a set X, mu:S->[0,infty] a set function, and mu^* the outer measure induced by mu. The measure mu^_ that is the restriction of mu^* to the ...

A graph is said to be unswitchable if it cannot be reduced to another graph with the same degree sequence by edge-switching. Conversely, a graph that can be reduced to ...

The base 16 notational system for representing real numbers. The digits used to represent numbers using hexadecimal notation are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, ...

A split graph is a graph whose vertices can be partitioned into a clique and an independent vertex set. Equivalently, it is a chordal graph whose graph complement is also ...

Suppose that V is a group representation of G, and W is a group representation of H. Then the vector space tensor product V tensor W is a group representation of the group ...

A connected set is a set that cannot be partitioned into two nonempty subsets which are open in the relative topology induced on the set. Equivalently, it is a set which ...

Let |z| be a vector norm of a vector z such that ||A||=max_(|z|=1)||Az||. Then ||A|| is a matrix norm which is said to be the natural norm induced (or subordinate) to the ...

The pair group of a group G is the group that acts on the 2-subsets of {1,...,p} whose permutations are induced by G. Pair groups can be calculated using PairGroup[g] in the ...