Definition of topology space
A topology $\mathcal T$ on a set $X$ is a collection of subsets of $X$ such that i) $\emptyset,X\in\mathcal T$ ii)if $O_\alpha\in\mathcal T$ for each $\alpha\in A$, then $\bigcup_{\alpha\in A}O_\alpha \in \mathcal T$. iii) if $O_1,...,O_n \in \mathcal T$, then $O_1\cap...\cap O_n\in \mathcal T$. A set $O\subseteq X$ is called open if $O\in \mathcal T$. The pair $(X,\mathcal T)$ is called topological space.
Basically any set in the topological space is open by definition. The textbook I am reading also lists out the way to define topological space by closed sets. I understand that part. In the textbook, then closed set is defined as
A subsef $F$ in $(X,\mathcal T)$ is called closed if $X-F$is open, that is, $X-F\in \mathcal T$
So if a set is closed, then it must be clopen in the topological space, am i right? There is not set which is neither closed or open in any topological space? It doesn't sound right. Does the textbook have a typo?