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I am studying real analysis and specially is about continuous and uniformly continuous.

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1. We say f : X → Y is Lipschitz continuous if ∀x, y ∈ X, ∃ C ∈ R such that dY (f (a), f (b)) ≤
CdX (a, b).
(a) Let > 0 be any given number.
∀a, b ∈ X such that dx (a, b) < C...

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