Abstract
In this paper we study some properties of the semi‐sub‐hypergroups and the closed sub‐hypergroups of the hypergroups. We introduce the correlated elements and the fundamental elements and we connect the concept antipodal of the latter with Frattin′s hypergroup. We also present Helly′s Theorem as a corollary of a more general Theorem.
Highlights
In this paper we study some properties of the seml-sub-hypergroups and the closed sub-hypergroups of the hypergroups
A sub-hypergroup K of fi is called closed from the right, if a.K N K
For the closed sub-hypergroups thls proposition is valid: K is closed from the right if and only if the relation a.(NK * implies that a e k
Summary
There are a,b e K such that a e x.b, x e a:b and since a:b_K, we have x e K. Let K be a closed sub-hypergroup of a hypergroup and let a K. Since K is a closed sub-hypergroup we have K: a _K. The proof of the other equality is analogous to this one. Let E be a subset of a hypergroup (H,.) [E], < E > will signify, the seml-sub-hypergroup and the closed sub-hypergroup of (H,.), respectively, which is. Let H,K be two closed sub-hypergroups of a hypergroup .
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