Topological definition of continuity is same as epsilon delta definition
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| A is ϵ -open } is a topology on . This way, every metric on a space induces atopology on . Now using the definition of continuity that only needs a concept of open sets, we can generalize the notion of a continuous function between two metric spaces to acontinuous function between twotopological spaces.
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general-topology metric-spaces continuity definition epsilon-delta. Claim: A function f:X→Y is continuous if given any open set U⊆Y the inverse image f−1(U)⊆X is open.
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