<p>Let T = (<strong>T</strong>, ≤) and T₁= (<strong>T</strong>₁ , ≤₁) be linearly ordered sets and X be a topological space. The main result of the paper is the following: If function ƒ(t,x) : <strong>T</strong> × X → <strong>T</strong>₁is continuous in each variable (“t” and “x”) separately and function ƒ_x(t) = ƒ(t,x) is monotonous on <strong>T</strong> for every x ∈ X, then ƒ is continuous mapping from<strong> T</strong> × X to <strong>T</strong>₁, where <strong>T</strong> and <strong>T</strong>₁ are considered as topological spaces under the order topology and <strong>T</strong> × X is considered as topological space under the Tychonoff topology on the Cartesian product of topological spaces <strong>T</strong> and X.</p>