Peritopological Spaces and Bisimulations
Hamal Ahmet, Terziler Mehmet
Abstract:
Generalizing ordinary topological and pretopological spaces, we
introduce the notion of peritopology where neighborhoods of a point
need not contain that point, and some points might even have an empty
neighborhood. We brieﬂy describe various intrinsic aspects of this
notion. Applied to modal logic, it gives rise to peritopological
models, a generalization of topological models, a spacial case of
neighborhood semantics. (In a last section, the relation between the
latter and the former is discussed, cursorily). A new cladding for
bisimulation is presented. The concept of Alexandroﬀ peritopology is
used in order to determine the logic of all peritopological spaces,
and we prove that the minimal logic K is strongly complete with
respect to the class of all peritopological spaces. We also show that
the classes of T0 , T1 and T2 -peritopological spaces are not modal
deﬁnable, and that D is the logic of all proper peritopological
spaces.
Keywords: peritopological spaces; bisimulations; modal definability