Abstract: This chapter discusses initially κ-compact and related spaces. A main reason for studying initial κ and, more generally, interval compactness is that compactness, countable compactness, and the Lindelöf property are special cases of one or both of these concepts. Another reason is that the theory of initially κ-compact and related spaces provides a means for answering fundamental questions that arise in other areas of topology. A third reason is that results in this area illustrate the usefulness of the close relationship that exists between the set theory of uncountable cardinals and properties of topological spaces. A space is countably compact if and only if it is initially ω-compact, and it is Lindelöf if and only if it is finally ω1-compact. Like compactness, initial κ-compactness is preserved by continuous mappings, perfect pre-images, and closed subsets.
Publication Year: 1984
Publication Date: 1984-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 48
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