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S1.4

math.toronto.edu · 3,658 words · saved by 1 readers

Definition. A set S⊂ ℝ n S⊂Rn is said to be compact if every sequence in S S has a subsequence that converges to a limit in S S .

S1.4 1.4: Compactness and related topics $\newcommand{\R}{\mathbb R }$ $\newcommand{\N}{\mathbb N }$ $\newcommand{\Z}{\mathbb Z }$ $\newcommand{\bfa}{\mathbf a}$ $\newcommand{\bfb}{\mathbf b}$ $\newcommand{\bff}{\mathbf f}$ $\newcommand{\bfu}{\mathbf u}$ $\newcommand{\bfx}{\mathbf x}$ $\newcommand{\bfy}{\mathbf y}$ $\newcommand{\ep}{\varepsilon}$ Compactness and applications. Compactness the Extreme Value Theorem Uniformly continuous functions Uniform continuity and compactness Problems Compactness Definition . A set $S\subset \R^n$ is said to be compact if every sequence in $S$ has a subseque

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