Definition: Pointwise and Uniform Convergence

Let \((X,d)\) and \((Y,d)\) be metric spaces, let \(f:X\to Y\) be a function and let \(f_n:X\to Y\), \(n\in\mathbb N\) be a sequence of functions.

Please note that the difference between pointwise and uniform convergence is that in the first case the index \(N\) depends on both, \(x\) and \(\epsilon\), while in the latter case it only depends on \(\epsilon\).

Examples: 1 Corollaries: 1

Corollaries: 1
Examples: 2

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  1. Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984