Question: A functional f: X is continuous if and only if its upper f (a) = {x: f (x) > a} and lower contour

A functional f: X → ℜ is continuous if and only if its upper
≿f (a) = {x: f (x) > a}
and lower contour sets
≿f (a) = {x: f (x) ≤ a}
are both closed.

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