We propose a functional description of rewriting systems on topological vector spaces. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting systems with continuous reduction operators, we show that the topological confluence is characterised by lattice operations. We relate these operations to standard bases and show that the latter induce topologically confluent rewriting systems on formal power series. Finally, we investigate duality for reduction operators that we relate to series representations and syntactic algebras. In particular, we use duality for proving that an algebra is syntactic or not.

中文翻译：

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应用于标准基础和句法代数的拓扑重写系统

我们提出了在拓扑向量空间上重写系统的功能描述。我们引入拓扑汇合性质作为汇合性质的近似。使用具有连续归约算子的线性拓扑重写系统的表示，我们表明拓扑汇合以格运算为特征。我们将这些操作与标准基联系起来，并表明后者在形式幂级数上诱导拓扑融合重写系统。最后，我们研究了与级数表示和句法代数相关的归约算子的对偶性。特别是，我们使用对偶来证明代数是否符合句法。