A net is a family indexed by a directed ordered set: every pair of indices has a common upper bound. It converges to when it is eventually in every neighbourhood of . Unlike sequences, nets characterize closure in every topological space: a point is in the closure of a set precisely when some net in that set converges to it.
In mathematics, the term "net" can refer to several different concepts, depending on the context. Here are two of the most common interpretations: 1. **Net in Topology**: In topology, a net is a generalization of a sequence that allows the indexing of elements by a directed set. While a sequence is indexed by the natural numbers, a net can be indexed by any directed set, which gives it more flexibility.
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