  Equational Artinian algebras were introduced in our previous work: {\em
Equational conditions in universal algebraic geometry, to appear in Algebra and
Logic, 2015}. In this note, we define the notion of {\em radical topology with
respect to an algebra $A$} and using the well-known K\"onig 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.
