In this paper, we introduce a new class of open balls in an m-metric space (X; μ) which will form a base for a Hausdorff topology on X. This will facilitate the initiation of open and closed sets, neighbourhoods and other allied notions in m-metric spaces. Moreover, we discuss the regularity and first countability properties of m-metric spaces and prove Cantor's intersection theorem, Baire's category theorem, Urysohn's lemma in the setting of m-metric spaces.