H-closed functions
The notion of a Hausdorff function is generalized to the concept of H-closed function and the concept of an H-closed extension of a Hausdorff function is developed. Each Hausdorff function is shown to have an H-closed extension.
Hereditarily normal Katětov spaces and extending of usco mappings
Several classes of hereditarily normal spaces are characterized in terms of extending upper semi-continuous compact-valued mappings. The case of controlled extensions is considered as well. Applications are obtained for real-valued semi-continuous functions.