International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 423-432

On the inverse image of Baire spaces

Mustafa Çiçek

Department of Mathematics, Faculty of Science, Ankara University, Beşvler, Ankara 06100, Turkey

Received 18 September 1995; Revised 12 March 1996

Copyright © 1997 Mustafa Çiçek. 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.


In 1961, Z. Frolik proved that if f is an open and continuous mapping of a metrizable separable space X onto Baire space Y and if the point inverses are Baire spaces, then X is a Baire space. We give a generalization to semi-continuous and semi-open mapping of this theorem and extended it to the several types of mappings.