This paper is devoted 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 the categorical sense. Also, we introduce the notion of semi-locally small loop space which is the necessary and sufficient condition for existence of universal covering for non-homotopically Hausdorff spaces, equivalently existence of small covering spaces. Moreover, we prove that for semi-locally small loop spaces, $X$ is a small loop space if and only if every covering of $X$ is trivial if and only if $\\pi_1^{top}(X)$ is an indiscrete topological group.

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