We prove the following theorem: THEOREM. Let Y be a second countable, infinite R 0 -space. If there are countably many open sets 0 1 , 0 2 , … , 0 n , … in Y such that 0 1 ⫋ 0 2 ⫋ … ⫋ 0 n ⫋ … , then a topological space X is a Baire space if and only if every mapping f : X → Y is almost continuous on a dense subset of X . It is an improvement of a theorem due to Lin and Lin [2].