Abstract: Covering approximation spaces is a class of important
generalization of approximation spaces. For a subset X of a covering
approximation space (U, C), is X definable or rough? The
answer of this question is uncertain, which depends on covering
approximation operators endowed on (U, C). Note that there are many
various covering approximation operators, which can be endowed
on covering approximation spaces. This paper investigates covering
approximation spaces endowed ten covering approximation operators
respectively, and establishes some relations among definable subsets,
inner definable subsets and outer definable subsets in covering approximation
spaces, which deepens some results on definable subsets
in approximation spaces.