| 释义 |
net A generalization of a sequence. Whilst the topology of a metric space can be characterized by sequences, this is not generally true in topological spaces. A net (xλ) in a topological space X consists of points indexed by a set (Λ,≤) with the properties (i) λ≤λ for all λ (ii) if λ1≤λ2 and λ2≤λ3, then λ1≤λ3 (ii) for any λ1,λ2 there exists λ3 such that λ1≤λ3 and λ2≤λ3. A net (xλ) then converges to x if for any open set U containing x, there exists μ such that whenever μ≤λ, then xλ is in U. Then, for example, x is in the closure of a set A if and only there is a net in A which converges to x.
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