κ‐Structures: Cardinality Conditions, Compactness, Metrization | Zendy

HODEL R. E. | Zendy

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κ‐Structures: Cardinality Conditions, Compactness, Metrization

Author(s) -

HODEL R. E.

Publication year - 1992

Publication title -

annals of the new york academy of sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.712

H-Index - 248

eISSN - 1749-6632

pISSN - 0077-8923

DOI - 10.1111/j.1749-6632.1992.tb32252.x

Subject(s) - metrization theorem , compact space , cardinality (data modeling) , mathematics , generalization , diagonal , space (punctuation) , extension (predicate logic) , pure mathematics , set (abstract data type) , discrete mathematics , topology (electrical circuits) , combinatorics , mathematical analysis , separable space , computer science , geometry , data mining , programming language , operating system

The notion of a κ‐structure on a set E is introduced as a generalization of a topology on E . Pospíšil's inequality | X |≤ d(X) χ( X ) , Arhangel'skiĭi's inequality | X |≤ 2 L(X)χ(X) , and Gryzlov's inequality | X |≤ 2 ψ( X ) for X compact all extend to κ‐structures. Chaber's theorem, that every countably compact space with a G δ ‐diagonal is compact, also extends to κ‐structures. Two metrization theorems in terms of κ‐structures are given.

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