Abstract
<p>Let T = (<strong>T</strong>, ≤) and T<sub>1</sub>= (<strong>T</strong><sub>1</sub> , ≤<sub>1</sub>) 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><sub>1 </sub>is continuous in each variable (“t” and “x”) separately and function ƒ<sub>x</sub>(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><sub>1</sub>, where <strong>T</strong> and <strong>T</strong><sub>1</sub> 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>
Publisher
Universitat Politecnica de Valencia
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