Date of Award
University or Center
Atlanta University (AU)
Mr. John Boyd, Jr.
A topological space X is compact-finite if and only if compactness and finiteness are equivalent. The most commonly used term for such a space is cf. CF-spaces may be determined in many ways. However, to show that a space is cf, it suffices to prove that every compact set is finite or that every infinite set is not compact. Numerous examples and related theorems of cf-spaces are presented.
Rivas, Ethel L. Wright, "On the equivalence of compactness and finiteness in topology" (1970). ETD Collection for AUC Robert W. Woodruff Library. 2817.