$f$ is continuous function when $x \in [a,b]$ show that $M(x)=\sup\{ f(y):y \in [a,x]\}$ is continuous in $[a,b]$
Can someone help me to prove this ?
It seems simple but I can`t get started. I was far from real analysis for years, I Did not find a clue
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saulspatz
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Khosrotash
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Start by writing down what you have to prove, in terms of $\varepsilon$ and $\delta.$ – saulspatz Apr 12 '20 at 15:41