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Small loop spaces and covering theory of non-homotopically Hausdorff spaces
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 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, is a small
loop space if and only if every cover of is trivial if and only if
is an indiscrete topological group.Comment: 7 page
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