학술저널
A CORRECTION OF KELLEY’S PROOF ON THE EQUIVALENCE BETWEEN THE TYCHONOFF PRODUCT THEOREM AND THE AXIOM OF CHOICE
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 16, No. 2
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2003.111 - 5 (5 pages)
- 3
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.
1. Introduction
2. Analysis of the Kelley’s proof
3. Correction of the proof
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