LAUSR

Let T = (T, ≤) and T₁= (T₁ , ≤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) : T × X → T₁ is continuous in each  variable (“t” and  “x”)  separately  and  function ƒ_x(t)  = ƒ(t,x) is  monotonous  on T for  every x ∈ X,  then ƒ is  continuous  mapping  from T × X to T₁,  where T and T₁ are  considered  as  topological  spaces  under  the order topology and T × X is considered as topological space under the Tychonoff topology on the Cartesian  product of topological spaces T and X.