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What is a continuous function in a topological sense? Sure, everyone knows the classic ε-δ definition for continuity but what do we do when we don’t have a metric? My professor calls this theorem the “gateway” to topology because this is our opening, continuity defined purely in open sets. The proof is pretty simple to follow along with so hopefully you enjoy. #math #topology #metricspace #continuity #realanalysis
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What is a continuous function in a topological sense? Sure, everyone knows the classic ε-δ definition for continuity but what do we do when we don’t have a metric? My professor calls this theorem the “gateway” to topology because this is our opening, continuity defined purely in open sets. The proof is pretty simple to follow along with so hopefully you enjoy. #math #topology #metricspace #continuity #realanalysis
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Q) Show that the function 𝑓(𝑥)={(cos𝑥/(−𝑥+𝜋/2), 𝑥≠𝜋/2 1, 𝑥=𝜋/2 is continuous at x=𝜋/2.
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