Existence of Zeros via Disconnectedness

The purpose of this short paper is very modest if compared with the greatness of the mathematician to whom it is dedicated. Here, indeed, we wish only to signalize a new result on the existence of zeros for operators taking their values in the dual of a real topological vector space. We do hope, however, that the novelty together with the simplicity of its statement can draw the attention of other mathematicians, in order to discover a possible variety of intermediate conditions making easier its applicability to concrete situations.