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Topological Properties of Forbidding-Enforcing Systems

Forbidding-enforcing systems (fe-systems) define classes of languages (fe-families) based on boundary conditions. We characterize f-families having not necessarily finite forbidders and prove that none of the Chomsky families of languages can be defined with an fe-system, hence, fe-systems provide a completely new way of defining classes of languages. We show that f-families map to f-families by morphic maps if and only if the morphism maps symbol to symbol. A morphism mapping e-families to e-families is necessarily surjective.