International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 695-699
On barely continuous functions
Department of Applied Mathematics, Western Carolina University, Cullowhee 28723, NC, USA
Received 23 March 1987
Copyright © 1988 Richard Stephens. 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.
The term barely continuous is a topological generalization of Baire- according to . Gerlits of the Mathematical Institute of the Hungarian Academy of Sciences, and thus worthy of further study. This paper compares barely continuous functions and continuous functions on an elementary level. Knowing how the continuity of the identity function between topologies on a given set yields the lattice structure for those topologies, the barely continuity of the identity function between topologies on a given set is investigated and used to add to the structure of that lattice. Included are certain sublattices generated by the barely continuity of the identity function between those topologies. Much attention is given to topologies on finite sets.