An Overview of Topological and Fuzzy Topological Hypergroupoids

Sarka Hosková-Mayerová


On a hypergroup, one can define a topology such that the hyperoperation is pseudocontinuous or continuous.
This concepts can be extend to the fuzzy case and a connection between the classical and the fuzzy (pseudo)continuous hyperoperations can be given.
This paper, that is his an overview of results received by S. Hoskova-Mayerova with coauthors  I. Cristea , M. Tahere and  B. Davaz, gives examples of topological hypergroupoids and show that there is no relation (in general) between pseudotopological and strongly pseudotopological hypergroupoids. In particular, it shows a topological hypergroupoid that does not depend on the pseudocontinuity nor on strongly pseudocontinuity of the hyperoperation.


Hyperoperation; hypergroupoid; continuous; pseudocontinuous and strongly pseudocontinuous hyperoperation; topology; topological hypergroupoid; (fuzzy) pseudocontinuous hyper\-operation; (fuzzy) continuous hyperoperation; fuzzy topological space.

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