International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 1, Pages 197-199

A note of almost continuous mappings and Baire spaces

Jing Cheng Tong

Department of Mathematics, Wayne State University, Detroit 48202, Michigan, USA

Received 20 April 1982; Revised 4 June 1982

Copyright © 1983 Jing Cheng Tong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 01020n, then a topological space X is a Baire space if and only if every mapping f:XY is almost continuous on a dense subset of X. It is an improvement of a theorem due to Lin and Lin [2].