I have a weakness for pictures. So here is one

function http://pages.bangor.ac.uk/%7Emas010/compactopen2.jpg

The above shows a function $f: \mathbb R \to \mathbb R$, a compact set $C$, and an open set $U$. The condition $f(C) \subseteq U$ is that the graph of $f$ passes through the shaded part shown in the picture.

I have a weakness for pictures. So here is one

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The above shows a function $f: \mathbb R \to \mathbb R$, a compact set $C$, and an open set $U$. The condition $f(C) \subseteq U$ is that the graph of $f$ passes through the shaded part shown in the picture.

I have a weakness for pictures.

function http://pages.bangor.ac.uk/%7Emas010/compactopen.jpg

The above shows a function $f: \mathbb R \to \mathbb R$, a compact set $C$, and an open set $U$. The condition $f(C) \subseteq U$ is that the graph of $f$ passes through the shaded part shown in the picture.

I have a weakness for pictures. So here is one

function http://pages.bangor.ac.uk/%7Emas010/compactopen2.jpg

The above shows a function $f: \mathbb R \to \mathbb R$, a compact set $C$, and an open set $U$. The condition $f(C) \subseteq U$ is that the graph of $f$ passes through the shaded part shown in the picture.