The Tychonoff product theorem for compact Hausdorff spaces does not imply the axiom of choice: A new Proof. equivalent propositions.
Collectanea mathematica, Tome 24 (1973) no. 3.

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     author = {Salinas, B. R. and  Bombal, F.},
     title = {The {Tychonoff} product theorem for compact {Hausdorff} spaces does not imply the axiom of choice: {A} new {Proof.} equivalent propositions.},
     journal = {Collectanea mathematica},
     pages = {219-230},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {1973},
     zbl = {0279.04003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CLTM_1973_1973_1_a17/}
}
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Salinas, B. R.;  Bombal, F. The Tychonoff product theorem for compact Hausdorff spaces does not imply the axiom of choice: A new Proof. equivalent propositions.. Collectanea mathematica, Tome 24 (1973) no. 3. http://geodesic.mathdoc.fr/item/CLTM_1973_1973_1_a17/