Open interval : An open interval $(a,b)$ consists of all numbers $x$ with $a\lt x\lt b.$ In contrast to a closed interval the endpoints of the interval $a$ and $b$ are not part of the interval. A continuous function does not necessarily attain a maximum and a minimum in an open interval. For example the function $f(x)=x$ does not attain the maximum or minimum in the open interval (0,1).