On the equational Artinian algebras

Equational Artinian algebras were introduced in our previous work: Compactness conditions in universal algebraic geometry, Algebra and Logic, 2016, 55 (2). In this note, we define the notion of radical topology with respect to an algebra $A$ and using the well-known König lemma in graph theory, we show that the algebra $A$ is equational Artinian iff this topology is Noetherian. This completes the analogy between equational Noetherian and equational Artinian algebras.