Communications of the
Korean Mathematical Society CKMS

In this paper we adhere to the definition of emph{infra-topological} space as it was introduced by Al-Odhari. Namely, we speak about families of subsets which contain $emptyset$ and the whole universe $X$, being at the same time closed under finite intersections (but not necessarily under arbitrary or even finite unions). This slight modification allows us to distinguish between new classes of subsets (infra-open, ps-infra-open and i-genuine). Analogous notions are discussed in the language of closures. The class of minimal infra-open sets is studied too, as well as the idea of generalized infra-spaces. Finally, we obtain characterization of infra-spaces in terms of modal logic, using some of the notions introduced above.

Keywords: Generalized topological spaces, infra-topological spaces, modal logic

MSC numbers: Primary 54A05; Secondary 03B45