International Journal of Mathematics and Mathematical Sciences 
Volume 20 (1997), Issue 3, Pages 423-432
doi:10.1155/S0161171297000586

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

Abstract

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.