  In this paper we devote to spaces that are not homotopically hausdorff and
study their covering spaces. We introduce the notion of small covering and
prove that every small covering of $X$ is the universal covering in categorical
sense. Also, we introduce the notion of semi-locally small loop space which is
the necessary and sufficient condition for existence of universal cover for
non-homotopically hausdorff spaces, equivalently existence of small covering
spaces. Also, we prove that for semi-locally small loop spaces, $X$ is a small
loop space if and only if every cover of $X$ is trivial if and only if
$\pi_1^{top}(X)$ is an indiscrete topological group.
