Hashem Bordbar

You are already at the latest version The notion of a nodal filter has recently gained attention. A filter is called nodal (of type 1) if it is a node in the poset of all filters ordered by inclusion. This seemingly simple order- theoretic condition imposes a strong rigidity on the filter lattice and makes nodal filters natural candidates for serving as reference points or “skeletons” within the filter structure. The present work performs a systematic study of nodal filters in equality algebras.

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1. Introduction Let H be a nonempty set and P * ( H ) be the set of nonempty subsets of H. The map ∘ : H × H ⟶ P * ( H ) is referred to as hyperoperation on H. Thus, for the element a , b ∈ H , a ∘ b is not a single element, as the result of a classical operation, yet is a nonempty subset of the set H.