continuous bounded function space

[[concept]]

C_{\infty} (X)

If $X$ is a vector space, the vector space

C_{\infty} (X) = {f : X \to C | f is continuous and bounded}

Example

$C_{\infty} ([0, 1]) = C ([0, 1])$ since we know the set $X$ is bounded

this is a normed vector space

Mentions

File	Last Modified
complete metric spaces have banach continuous bounded function spaces	2025-10-02
continuous linear function space	2025-10-02
Functional Analysis Lecture 1	2025-10-02

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