Section 18. Continuous Functions
Jun 11, 2016 · Note. As you can see in the proof of the previous theorem, we can replace “closed” with “open” to get the following. Corollary 18.A. The Pasting Lemma for Open Sets. Let X = A∪ B where A and B are open in X. Let f : A → Y and g : B → Y be continuous. If f(x) = g(x) for all x ∈ A ∪ B, then f and g combine (or “paste”)
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