Abstract
Sequence-covering and countably bi-quotient mappings are studied and used to characterize sequential, Fréchet, strong accessibility, strongly Fréchet, and strongly k′-spaces. A sequence-covering mapping has a definition analogous to that of a compact-covering mapping, while a countably bi-quotient mapping is a weakening of a bi-quotient mapping. Strong accessibility, strongly Fréchet, and strongly k′-spaces, each generalizations of first countability, are also studied.
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