• 대한수학회논문집
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• 제13권1호
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• pp.61-72
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• 1998

It has been known that if T and S are even Kakutani equivalent, then there exists U such that T and U are $\alpha$-equivalent and S and U are $\beta$-equivalent where $\alpha$ and $\beta$ are irrationally related. In this paper we give a complete discrete proof of this theorem without using R-actions.

• 충청수학회지
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• 제16권2호
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• pp.75-78
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• 2003

The Tychonoff product theorem is one of the most fundamental theorems in general topology. As is well-known, the proof of the Tychonoff product theorem relies on the axiom of choice. The converse was also conjectured by S. Kakutani and Kelley [1] then resolved this conjecture in his historical short note on 1950. However, the original proof due to Kelley has a flaw. According to this observation, we provide a correction of the proof in this paper.