Generalized approximation spaces

Generalized approximation spaces may be considered as a generalization of approximation spaces invented by Pawlak in the context of his rough sets theory. Here we discuss some basic relationships between these spaces and topology. This presentation is based on two papers: one by T. K. Sheeja and A. Sunny Kuriakose ("Continuity on approximation spaces") and one by Z. Pei, D. Pei, L. Zhen ("Topology vs generalized rough sets"). A vast majority of definitions, notions, symbols, theorems and examples is taken from the first paper.