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

Preview |
Text (Full Text)
PP-2009-29.text.pdf Download (157kB) | Preview |

Text (Abstract)
PP-2009-29.abstract.txt Download (1kB) |

## 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 |

## Actions (login required)

View Item |