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A ~ B ⇒ f(A) ~ f(B) for f continuous
(In the ε-δ-world it's probably faster to show the equivalence to the open set definition rather than stepping through.)
... So taking g as the path between A and B, f⋅g defines the path between f(A) and f(B).FactChecker said:... so f(g) is continuous.
(In the ε-δ-world it's probably faster to show the equivalence to the open set definition rather than stepping through.)
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