Equivalence among the Banach-Alaoglu theorem, Ascoli- Arzela theorem and Tychonoff's theorem

Abstract

This article is meant to serve as a bridge among these three theorems. The similarity among  Banach-Alaoglu theorem, Ascoli-Arzela theorem,  and the Tychonoff's theorem are proved. Banach- Alaoglu theorem, Ascoli-Arzela theorem are derived as an immediate consequence of the Tychonoff theorem. These all theorems are compact and equicontinuous and compact Hausdorff spaces are equivalent.