Premium
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.