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We propose a functional description of rewriting systems on topologicalvector spaces. We introduce the topological confluence property as anapproximation of the confluence property. Using a representation of lineartopological rewriting systems with continuous reduction operators, we show thatthe topological confluence is characterised by lattice operations. We relatethese operations to standard bases and show that the latter inducetopologically confluent rewriting systems on formal power series. Finally, weinvestigate duality for reduction operators that we relate to seriesrepresentations and syntactic algebras. In particular, we use duality forproving that an algebra is syntactic or not.

Topological rewriting systems applied to standard bases and syntactic algebras