The Alaoglu Theorem for topological $\mathbb{BC}-$module

Authors

  • Amjad Ali Department of Mathematics, University of Jammu, Jammu 180 001, India
  • Aditi Sharma Department of Mathematics, University of Jammu, Jammu, J&K - 180 006, India

DOI:

https://doi.org/https://doi.org/10.31392/MFAT-npu26_3–4.2023.01

Keywords:

$\mathbb{BC}$-modules, $\mathbb{D}$-modules, product-type set, hyperbolic numbers, $\mathbb{D}$-convex, $\mathbb{BC}$-convex function

Abstract

In this paper we prove the bicomplex version of the Alaoglu theorem for a topological $\mathbb{BC}$-module $X$. The concept of a $\mathbb{BC}$-dual pair and a product-type open cover in bicomplex is also introduced.

Доведено бікомплексну версію теореми Alaoglu у топологічному $\mathbb{BC}$-модулі $X.$ Також наведено поняття про $\mathbb{BC}$-дуальну пару та відкрите покриття типу добутку в бікомплексі.

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Published

2023-09-25

Issue

Vol. 29 No. 3-4 (2023)

Section

Articles

How to Cite

Ali, Amjad, and Aditi Sharma. “The Alaoglu Theorem for Topological $\mathbb{BC}-$module”. Methods of Functional Analysis and Topology, vol. 29, no. 3-4, Sept. 2023, pp. 83–93, https://doi.org/https://doi.org/10.31392/MFAT-npu26_3–4.2023.01.