EDB β€” 0T7

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Exercises

  1. [0T7] Let \(AβŠ‚β„^ n\) be a bounded set. For every \(\varepsilon {\gt}0\) there is a set \(IβŠ‚ A\) that satisfies:

    • \(I\) is a finite set,

    • \(βˆ€ x,y∈ I\), \(xβ‰  y\) you have \(xβˆ‰ B(y,\varepsilon )\) (i.e. \(d(x,y)β‰₯ \varepsilon \)),

    • \[ AβŠ† ⋃_{x∈ I} B(x,\varepsilon )~ ~ . \]

    Solution 1

    [0T8]

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