Supplementary Definitions
Let φ be a net on X based on the directed set D and let A be a subset of X, then φ is said to be frequently in (or cofinally in) A if for every α in D there exists some β ≥ α, β in D, so that φ(β) is in A.
A point x in X is said to be an accumulation point or cluster point of a net if (and only if) for every neighborhood U of x, the net is frequently in U.
A net φ on set X is called universal, or an ultranet if for every subset A of X, either φ is eventually in A or φ is eventually in X-A.
Read more about this topic: Net (mathematics)
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