%0 Journal Article
%T Small loop spaces and covering theory of non-homotopically Hausdorff spaces
%A Ali Pakdaman
%A Hamid Torabi
%A Behrooz Mashayekhy
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1011.1611v1