Partial-congruence factorization of bisimilarity induced by open maps

1998 ◽  
pp. 91-102 ◽  
Author(s):  
Slawomir Lasota
Keyword(s):  
Open Maps

Certain new kinds of αrps - open maps in topological spaces

2021 ◽  
pp. 1-8
Author(s):  
Dunya Mohamed Hameed ◽  
Intidhar Zamil Mushtt ◽  
Shimaa Mohammed Dawood
Keyword(s):  
Topological Spaces ◽  
Open Maps

scholarly journals Bisimulation from Open Maps

1994 ◽  
Vol 1 (7) ◽  
Author(s):  
André Joyal ◽  
Mogens Nielsen ◽  
Glynn Winskel
Keyword(s):  
Petri Nets ◽  
Parallel Computation ◽  
Transition Systems ◽  
New Model ◽  
Event Structures ◽  
Uniform Definition ◽  
Refinement Operators ◽  
Definition Of ◽  
Open Maps

An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of history-preserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tie-up with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has ``refinement'' operators, though further work is required to justify their appropriateness and understand their relation to previous attempts. The general approach yields a logic, generalising Hennessy-Milner logic, which is characteristic for the generalised notion of bisimulation.

scholarly journals A Presheaf Semantics of Value-Passing Processes

1996 ◽  
Vol 3 (44) ◽  
Author(s):  
Glynn Winskel
Keyword(s):  
Operational Semantics ◽  
Denotational Semantics ◽  
Domain Theory ◽  
Process Calculi ◽  
Traditional Definition ◽  
Open Maps

This paper investigates presheaf models for process calculi with<br />value passing. Denotational semantics in presheaf models are shown<br />to correspond to operational semantics in that bisimulation obtained<br />from open maps is proved to coincide with bisimulation as defined<br />traditionally from the operational semantics. Both "early" and "late"<br />semantics are considered, though the more interesting "late" semantics<br />is emphasised. A presheaf model and denotational semantics is proposed<br />for a language allowing process passing, though there remains<br />the problem of relating the notion of bisimulation obtained from open<br />maps to a more traditional definition from the operational semantics.<br />A tentative beginning is made of a "domain theory" supporting<br />presheaf models.

scholarly journals On R#-Closed and R#-Open Maps in Topological Spaces

2018 ◽  
Vol 7 (4.10) ◽  
pp. 770
Author(s):  
Raghavendra K ◽  
Basavaraj M. Ittanagi
Keyword(s):  
Topological Spaces ◽  
Open Maps

Defining and investigating properties of R#-closed maps, R#-open maps, R#*-closed maps and R#*-open maps in topological spaces.2010 Mathematics Classification: 54A05, 54A10 

scholarly journals A Representation Result for Free Cocompletions

1998 ◽  
Vol 5 (21) ◽  
Author(s):  
John Power ◽  
Gian Luca Cattani ◽  
Glynn Winskel
Keyword(s):  
Small Category ◽  
Representation Result ◽  
Open Maps ◽  
Class F

Given a class F of weights, one can consider the construction that<br />takes a small category C to the free cocompletion of C under weighted colimits, for which the weight lies in F. Provided these free Fcocompletions are small, this construction generates a 2-monad on Cat, or more generally on V-Cat for monoidal biclosed complete and cocomplete V. We develop the notion of a dense 2-monad on V-Cat and characterise free F-cocompletions by dense KZ-monads on V-Cat. We prove various corollaries about the structure of such 2-monads and their Kleisli 2-categories, as needed for the use of open maps in giving an axiomatic study of bisimulation in concurrency. This requires the introduction of the concept of a pseudo-commutativity for a strong 2-monad on a symmetric monoidal 2-category, and a characterisation of it in terms of structure on the Kleisli 2-category.

scholarly journals Soft(1, 2)-Strongly Open Maps in Bi-Topological Spaces

2019 ◽  
Vol 571 ◽  
pp. 012002 ◽  
Author(s):  
Abu Firas Muhamad Jawad Hasan al Musawi ◽  
Shuker Mahmood Khalil Al Salim ◽  
Mayadah Abd Ulrazaq
Keyword(s):  
Topological Spaces ◽  
Open Maps

scholarly journals Openness of vector measures and their integral maps

1988 ◽  
Vol 45 (3) ◽  
pp. 351-359 ◽  
Author(s):  
Andrzej Spakowski
Keyword(s):  
Vector Measures ◽  
Finite Dimensional ◽  
Open Maps

AbstractWe prove that finite dimensional nonatomic vector measures and their integral maps are open maps. These results can be found in the literature, but unfortunately the proofs presented there are not complete.

Continuous Open Maps on the Unit Interval

1969 ◽  
Vol 76 (7) ◽  
pp. 817-818
Author(s):  
S. S. Mitra
Keyword(s):  
Unit Interval ◽  
Open Maps

Light open maps on $n$ -manifolds. II

1961 ◽  
Vol 28 (4) ◽  
pp. 607-623 ◽  
Author(s):  
P. T. Church ◽  
E. Hemmingsen
Keyword(s):  
Open Maps
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