%0 Journal Article
%T Peritopological Spaces and Bisimulations
%A Hamal, Ahmet
%A Terziler, Mehmet
%J Reports on Mathematical Logic
%V 2015
%R 10.4467/20842589RM.15.005.3914
%N Number 50
%P 67-81

%@ 0137-2904
%D 2015
%U https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/peritopological-spaces-and-bisimulations
%X 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 brie y describe various intrinsic aspects of this notion. Applied to modal logic, it gives rise to peritopological models, a generalization of topo- logical models, a spacial case of neighborhood semantics. A new cladding for bisimulation is presented. The concept of Alexandro peritopology is used in order to determine the logic of all peritopo- logical 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 denable, and that D is the logic of all proper peritopological spaces. Finally, among our conclusions, we show that the question whether T0, T1 peritopological spaces are modal denable in H(@) remains open.