PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: High Entry average rating: High
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.
(view preamble)

View style:

Also defines:  pointwise
Log in to rate this entry.
(view current ratings)

Cross-references: converges, convergent, mapping, functions, sequence, topological space
There are 22 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 8385 times total.

Classification:
AMS MSC40A30 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Convergence and divergence of series and sequences of functions)

Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)