@article{Kumar_Raikhola_2024, title={The equivalency of the Banach-Alaoglu theorem and the axiom of choice }, volume={6}, url={https://nepjol.info/index.php/cognition/article/view/64440}, DOI={10.3126/cognition.v6i1.64440}, abstractNote={<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>}, number={1}, journal={Cognition}, author={Kumar, Nand Kishor and Raikhola, Sher Singh}, year={2024}, month={Apr.}, pages={60–64} }