Vol. 51, No. 2, 1974

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On k-quotient mappings

James Robert Boone

Vol. 51 (1974), No. 2, 369–377

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.

Mathematical Subject Classification 2000
Primary: 54C10
Secondary: 54D50
Received: 9 October 1973
Published: 1 April 1974
James Robert Boone