Pseudo-open functions are monotonic decreasing for ordinal and cardinal invariants

Abstract

A new property of pseudo-open functions is presented in this paper. Pseudo-open functions are monotonic decreasing with respect to ordinal and cardinal invariants defined by compact and sequential closures. A weak form of continuity, called k-continuous, is defined, characterized and used in the proof of the monotonicity properties of pseudo-open mappings. The relationships between the classes of k-continuous and sequentially continuous mappings in the category of all topological spaces and the continuous mappings in the subcategories of k-spaces and sequential spaces are presented.