[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ13 (1002ﾚｽ)
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409: 現代数学の系譜 雑談 ◆yH25M02vWFhP 02/09(日)09:54 ID:lz6oAIdr(4/12) AAS
つづき

There exist models of ZF that violate the above conditions ([17], [18]).
Observe the fine distinction between conditions 2 and 3 of Theorem 1.1.
These may lead one to assume that also the following property is equivalent to the above conditions:
(*) a function f : R −→ R is continuous iff it is sequentially continuous.
However, this would be a serious mistake: (*) holds in ZF (without any choiceassumptions) — see [29].
If, however, we consider functions f : X −→ R with metric domain we need even more choice than in Theorem 1.1, — see Theorem 2.1.
省27

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