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Topology question: Show that a function f : ℝ → ℝ is continuous in the ε...

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Advance Math

Topology question:

Show that a function f : ℝ → ℝ is continuous in the ε − δdefinition of continuity if and only if, for every x ∈ ℝ and everyopen set U containing f(x), there exists a neighborhood V of x suchthat f(V) ⊂ U.

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