Prove that if f(x) is a continuous function defined on [a,b] , then the set of points at which $f(x) \geq d$ is closed, for all numbers d.
2026-02-23 03:07:21.1771816041
For a continuous function defined on [a,b] , is the set of points at which f(x)>d closed set?
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The general topology definition of a continuous function $f$ says that $f^{-1}(F)$ is closed for any closed $F$. Is a set $[d,\infty)$ closed?