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The underlying set of the fundamental group of X is the set of based homotopy classes from the circle to X, denoted [S^1,X]. For general spaces X and Y, there is no natural ...

A definable set which is the complement of an analytic set.

Two open manifolds M and M^' are cobordant if there exists a manifold with boundary W^(n+1) such that an acceptable restrictive relationship holds.

A theorem that guarantees that the trajectory of Langton's ant is unbounded.

Two lines that lie on top of one another are called coincident lines.

An abbreviation for the cokernel.

The logarithm of the reciprocal of a number, equal to the negative of the logarithm of the number itself, cologx=log(1/x)=-logx.

An m×1 matrix [a_(11); a_(21); |; a_(m1)].

Combinatorial game theory is the theory of two-player games of perfect knowledge such as go, chess, or checkers.

The value of b, where a=b (mod m), taken to be nonnegative and smaller than m.