<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly preordered transpositions hypergroup of considered partial differntial operators.</p></abstract>

The contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly preordered transpositions hypergroup of considered partial differntial operators.

On Certain Proximities and Preorderings on the Transposition Hypergroups of Linear First-Order Partial Differential Operators

Department of Mathematics, Brno, University of Technology, Czech Republic.

Department of Mathematics and Physics, Brno, University of Defence, Czech Republic.

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup...

On Certain Proximities and Preorderings on the Transposition Hypergroups of Linear First-Order Partial Differential Operators

Published Online: Dec 10, 2014

Page range: 85 - 103

Received: Apr 01, 2013

Accepted: Aug 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0008

Keywords
Action of a hyperstructure on a set, semihypergroup, hypergroup, proximity space, transformation hypergroup, tolerance on a join space, regularly preordered hypergroup, ordered semigroup and group, partial differential operator

© 2014 Jan Chvalina and Šárka Hošková-Mayerová

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Certain Proximities and Preorderings on the Transposition Hypergroups of Linear First-Order Partial Differential Operators

Published Online: Dec 10, 2014

Page range: 85 - 103

Received: Apr 01, 2013

Accepted: Aug 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0008

KeywordsAction of a hyperstructure on a set, semihypergroup, hypergroup, proximity space, transformation hypergroup, tolerance on a join space, regularly preordered hypergroup, ordered semigroup and group, partial differential operator

© 2014 Jan Chvalina and Šárka Hošková-Mayerová

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Action of a hyperstructure on a set, semihypergroup, hypergroup, proximity space, transformation hypergroup, tolerance on a join space, regularly preordered hypergroup, ordered semigroup and group, partial differential operator