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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 diffeomorphism is a map between manifolds which is differentiable and has a differentiable inverse.

Distinguish between smooth manifolds in four dimensions.

An algorithm for computing an Egyptian fraction.

A problem in the theory of algebraic invariants that was solved by Hilbert using an existence proof.

A metric characterizing the difference between two knots K and K^' in S^3.

A type of integral named after Henstock and Kurzweil. Every Lebesgue integrable function is HK integrable with the same value.

A group having an infinite number of elements. Some infinite groups, such as the integers or rationals, are not continuous groups.

A bound on error-correcting codes.

A conjecture concerning primes.