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

Topology question:

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

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Colby Messinger answered 1 year ago

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