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

Authors

  • Nand Kishor Kumar Department of Mathematics, Trichandra College, Tribhuvan University, Nepal

DOI:

https://doi.org/10.3126/jie.v17i1.64587

Keywords:

Ascoli-Arzela theorem, Alaoglu theorem, Tychonoff's theorem, Product topology

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.

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Published

2023-04-12

How to Cite

Kumar, N. K. . (2023). Equivalence among the Banach-Alaoglu theorem, Ascoli- Arzela theorem and Tychonoff’s theorem. Journal of the Institute of Engineering, 17(1), 8–11. https://doi.org/10.3126/jie.v17i1.64587

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Section

Articles