충청수학회지 (Journal of the Chungcheong Mathematical Society)
- 제16권2호
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- Pages.75-78
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- 2003
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- 1226-3524(pISSN)
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- 2383-6245(eISSN)
A CORRECTION OF KELLEY'S PROOF ON THE EQUIVALENCE BETWEEN THE TYCHONOFF PRODUCT THEOREM AND THE AXIOM OF CHOICE
- Kum, Sangho (Department of Mathematics Education Chungbuk National University)
- 투고 : 2003.08.26
- 발행 : 2003.12.31
초록
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.