On the representation of nonseparable analytic sets

Hansell, R. W.

doi:10.1090/S0002-9939-1973-0380752-3

On the representation of nonseparable analytic sets
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Proc. Amer. Math. Soc. 39 (1973), 402-408 Request permission

Abstract:

Recently, the author considered extending the concepts of a Borel and analytic set for nonseparable metric spaces by allowing $\sigma$-discrete families to replace countable families in the classical definitions. The resulting class of “extended Borel sets” was shown to lead to a new class of sets, intermediate to the Borel and analytic sets. In the present paper we show that the corresponding class of “extended analytic sets” does not lead to a new class of sets but actually coincides with the standard class of analytic sets. Thus their importance lies in the fact that they provide a useful “representation” for the analytic sets in arbitrary spaces. Several such representations are shown to lead to the same class of analytic sets.

References

R. W. Hansell, On the nonseparable theory of Borel and Souslin sets, Bull. Amer. Math. Soc. 78 (1972), 236–241. MR 294138, DOI 10.1090/S0002-9904-1972-12936-7
Roger W. Hansell, On the non-separable theory of $k$-Borel and $k$-Souslin sets, General Topology and Appl. 3 (1973), 161–195. MR 319170

Mengenlehre

19

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