Abstract

We prove the following theorem: THEOREM. Let Y be a second countable, infinite R0-space. If there are countably many open sets 01,02,…,0n,… in Y such that 01⫋02⫋…⫋0n⫋…, 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].