Аннотация:In this chapter we study modal logics of topological spaces in the
combined language with the derivational modality and the difference modality. We
give axiomatizations and prove completeness for the following classes: all spaces,
T1-spaces, dense-in-themselves spaces, a zero-dimensional dense-in-itself separa5
ble metric space, Rn (n ≥ 2). We also discuss the correlation between languages
with different combinations of the topological, derivational, universal and difference
modalities in terms of definability.