Quasi-Order Hypergroups and T-Hypergroups

Šárka Hošková-Mayerová

Abstract


Quasi-order hypergroups were introduced by J. Chvalina in 90s of the last
century. They form a subclass of the class of all hypergroups, i.e. structures
with one associative hyperoperation fulfilling the reproduction axiom. In this
paper a theorem which allows an easy description of all quasi-order hyper-
groups is mentioned and some results concerning the relation of quasi-order
and upper quasi-order hypergroups are given. Furthermore the transformation
hypergroups acting on tolerance spaces are defined and an example of them is
given


Keywords


Quasi-order hypergroup; order hypergroup; tolerance relation; transformation semihypergroup; transformation hypergroup

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References


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DOI: http://dx.doi.org/10.23755/rm.v32i0.333

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.