In this paper we introduce and study the notion of ω^c-set. We also study ω-sets, as complements of ω^c-sets. Finally, using the ω^c-sets and ω-sets of a topological space, we introduce and study the notion of ω-extremally disconnected topological spaces. We obtain a result akin to Urysohn’s Lemma in the setting of ω-extremally disconnected top-ological spaces.
