A Topology on a Hyper BCI-algebra Generated by a Hyper-order

Michelle Panganduyon, Sergio Rosales Canoy Jr., Bijan Davvaz

Abstract

In this paper, we introduce an operator on a hyper BCI-algebra via application of a
left hyper-order. The family consisting of the images of subsets under the operator turns out to be a base for some topology on the hyper BCI-algebra. We investigate some important properties of the induced topology on certain hyper BCI-algebras. In particular, we show that the generated topology on a non-trivial hyper subalgebra of an ordered hyper BCI-algebra coincides with the relative topology on this hyper subalgebra.

Keywords

hyper BCI-algebra, topology, hyper order, hyperatom

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