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Let $(A,T)$ be a locally A-pseudoconvex algebra over $ℝ$ or $ℂ$. We define a new topology $m\left(T\right)$ on $A$ which is the weakest among all m-pseudoconvex topologies on $A$ stronger than $T$. We describe a family of non-homogeneous seminorms on $A$ which defines the topology $m\left(T\right)$.