International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 1, Pages 197-199
doi:10.1155/S0161171283000198
A note on almost continuous mappings and Baire spaces
Jing Cheng Tong
Department of Mathematics, Wayne State University, Detroit 48202, Michigan, USA
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].