EDB — 2B4

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Definition 3

[2B4] Given a net \(x:J\to Y\), a point \(z∈ Y\) is said to be a limit point for \(x\) if there is a subnet \(y:H\to Y\) such that \(\lim _{j\in H} y(j)=z\).

(Note that “subnet” is intended in the general sense presented at the end of [230], where \(y=x\circ i\) by means of a map \(i:H\to J\) satisfying [(7.iv.7)]).

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  • space, topological
  • topological space
  • limit point, of a net in a topological space
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