I am sorry in advance if this question is too naive for specialists. I just realized that I need it when doin research and I haven't taken any serious course on algebraic spaces. Let $u \colon U \longrightarrow X$ be an étale, separated morphism of alebraic spaces. Suppose that $u$ admits a section $s \colon X \longrightarrow U$, then it is similar to schemes that $s$ must be a closed immersion and étale. If we assume furthermore that $U$ is a scheme, then $s$ must be a closed, open immersion.
With schemes, we know that $s$ is an isomorphism onto a connected component of $U$, and $U = \operatorname{Im}(s) \sqcup X$. I am wondering whether we have a same decomposition in case $X$ an algebraic space (where no topological argument can be applied)?
