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pointwise convergence (Definition)

Let $ X$ be any set, and let $ Y$ be a topological space. A sequence $ f_1,f_2,\dots$ of functions mapping $ X$ to $ Y$ is said to be pointwise convergent (or simply convergent) to another function $ f$, if the sequence $ f_n(x)$ converges to $ f(x)$ for each $ x$ in $ X$. This is usually denoted by $ f_n\rightarrow f$.



"pointwise convergence" is owned by Koro.
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Also defines:  pointwise
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Cross-references: converges, convergent, mapping, functions, sequence, topological space
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This is version 1 of pointwise convergence, born on 2002-12-11.
Object id is 3737, canonical name is PointwiseConvergence.
Accessed 8385 times total.

Classification:
AMS MSC: 40A30 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Convergence and divergence of series and sequences of functions)
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