TY - JOUR
AU - Kumar, Nand Kishor
AU - Raikhola, Sher Singh
PY - 2024/04/08
Y2 - 2024/08/10
TI - The equivalency of the Banach-Alaoglu theorem and the axiom of choice
JF - Cognition
JA - Cognition
VL - 6
IS - 1
SE - Articles
DO - 10.3126/cognition.v6i1.64440
UR - https://nepjol.info/index.php/cognition/article/view/64440
SP - 60-64
AB - <p>The Axiom of Choice can be used to prove the Banach-Alaoglu theorem, while a weakened form of the Axiom of Choice is required to prove the full strength of the Hahn-Banach theorem, which is equivalent to the Banach-Alaoglu theorem. Although the Banach-Alaoglu theorem and the full- strength Axiom of Choice are not exactly equivalent, they are closely related.</p><p>The Banach-Alaoglu theorem is a compactness theorem whose proof mainly depends on Tychonoff's theorem. In this article, Banach-Alaoglu theorem is equivalent to the axiom of choice, has been proved.</p>
ER -