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Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

A quantity which is either 0 (zero) or positive, i.e., >=0.

A vector space possessing a norm.

A cupolarotunda in which the bases are in the same orientation.

The symbol p^e∥n means, for p a prime, that p^e|n, but p^(e+1)n.

A measure that takes on real values.

A reflexive relation.

One out of a set of identical observations in a given experiment under identical conditions.

Euclidean n-space is denoted R^n.

The robustness of a given outcome to small changes in initial conditions or small random fluctuations. Chaos is an example of a process which is not stable.