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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 strong inequality in which a is not only less than b, but much less (by some convention) is denoted a<<b.

A basis, form, function, etc., in two or more variables is said to be multilinear if it is linear in each variable separately.

If one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in mn ways.

A multiplication table is an array showing the result of applying a binary operator to elements of a given set S. For example, the following table is the multiplication table ...

n events are said to be mutually exclusive if the occurrence of any one of them precludes any of the others. Therefore, for events X_1, ..., X_n, the conditional probability ...

A 10000-sided polygon.

One of the two pieces of a double cone (i.e., two cones placed apex to apex).

mu_i(epsilon), sometimes denoted P_i(epsilon), is the probability that element i is populated, normalized such that sum_(i=1)^Nmu_i(epsilon)=1.

The simplicial complex formed from a family of objects by taking sets that have nonempty intersections.