A Characterization of a Certain Class of Compact Metric Spaces | Zendy

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A Characterization of a Certain Class of Compact Metric Spaces

Author(s) -

Feiste U.

Publication year - 1978

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19780830112

Subject(s) - mathematics , characterization (materials science) , metric space , class (philosophy) , compact space , field (mathematics) , metric (unit) , relatively compact subspace , locally compact space , space (punctuation) , injective metric space , discrete mathematics , pure mathematics , combinatorics , physics , linguistics , operations management , philosophy , artificial intelligence , computer science , optics , economics

Compact metric spaces χ of such a kind, that f =( X ), are characterized, ( X ) is the σ‐field of BOREL sets and f ( X ) is the field generated by all open subset of X . Our main result is Theorem 5: If χ is a compact metric space, then the following conditions are equivalent: 1 f ( X ) =( X ). 2 card ( X ) ≦ x 0 and there are k , m ϵ N such that card ( X ( k ) ) = m. 3 There are k , m ϵ N such that χ is homeomorphic to ω k · m + 1.

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