MV-Algebraic Moebius Transform on the Vietoris Space

Then it follows that mvm = m. Our main goal is to find an analogue of the Möbius transform on MV-algebras [4]. To this end, replace the boolean algebra 2X with a semisimple MV-algebra MX . There is no loss of generality in assuming that X is a compact Hausdorff space and MX is a separating MV-algebra of continuous functions over X. Since every Möbius transform mv corresponds to some finitely-additive measure on 2 2X , the many-valued counterpart of mv will be an MV-algebraic measure or state [7, 1]. Several problems arise in passing to a generalization of the combinatorial Möbius transform. How to replace the mapping A ∈ 2 7→ {B ∈ 2 | B ⊆ A } ∈ 22X (3)