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  1. Examples and counter-examples in analysis
    1. Pointwise convergence

    Examples and counter-examples in analysis

    Author:Vincent Pantaloni
    Topic:Continuity, Functions, Function Graph, Limits, Piecewise Functions, Power Functions, Sequences and Series, Trigonometric Functions
    Animations to illustrate lessons in analysis

    Pointwise convergence

    Some animations to illustrate what pointwise convergence is and some counter-examples regarding this notion.

    • Boundedness is not preserved by pointwise convergence.

    • Continuity is not preserved by pointwise convergence.

    • Differentiability is not preserved by pointwise convergence.

    • fn converges does not imply f'n converges

    • Integration counter-examples : Witch's hat functions

    • Integration and uniform convergence

    Next
    Boundedness is not preserved by pointwise convergence.

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