On the inverse image of Baire spaces

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.

Keywords

• Baire spaces
• second category spaces
• second countable space
• metrizable separable space
• almost-regular spaces
• nowhere dense set
• weakly-continuous
• semi-continuous
• almost-continuous
• feebly-continuous
• almost-open mapping
• semi-open mapping
• feebly-open mapping
• weakly-open mapping.