Two natural generalizations
of Arhangelśkiǐ’s compactcovering mappings are introduced, k-quotient and
k′-quotient mappings. These mappings may be used to replace the much stronger
perfect mappings in improving some mapping theorems concernin g the invariance of
topological structures. The defining k-systems and defining k1-systems of
Arhangelśkiǐ are fundamentally related to the k-quotient and k’-quotient
mappings. Functional characterizations of various k-spaces as domains and ranges of
certain mappings are presented. Examples are included to illustrate the results of this
study.
