PP-2009-29: Peritopological Spaces and Bisimulations

PP-2009-29: Ahmet, Hamal and Mehmet, Terziler (2009) Peritopological Spaces and Bisimulations. [Report]

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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.

Item Type: Report
Report Nr: PP-2009-29
Series Name: Prepublication (PP) Series
Year: 2009
Uncontrolled Keywords: peritopological spaces; bisimulations; modal definability
Subjects: Logic
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/359

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