Abstract: | 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) ≦x0 and there are k, m?N such that card (X(k)) = m.
- 3 There are k, m?N such that χ is homeomorphic to ωk · m + 1.
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