International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 1, Pages 197-199
doi:10.1155/S0161171283000198
A note of almost continuous mappings and Baire spaces
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.
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].