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pointwise convergence
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(Definition)
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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 $f_n\rightarrow f$
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"pointwise convergence" is owned by Koro.
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Cross-references: converges, convergent, mapping, functions, sequence, topological space
There are 25 references to this entry.
This is version 1 of pointwise convergence, born on 2002-12-11.
Object id is 3737, canonical name is PointwiseConvergence.
Accessed 9368 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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Pending Errata and Addenda
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