​​​​​​​January 2020, Vol. 5, No. 1, pp. 1-6. 

​​​On the significance of the Hahn-Banach theorem based on its historical background, formulation, implications, applications, and contributions

Amos Otieno Wanjara
School of Mathematics, Statistics, and Actuarial Science, Maseno University, Maseno, Kisumu, Kenya.

​​​*Corresponding author’s e-mail: awanjara78@gmail.com

​Abstract

​It is known that without the Hahn-Banach theorem, functional analysis would be very different from the structure we know today. Among other things, it has proved to be very appropriate form of the axiom of choice for analysts. In its elegance and power, the Hahn-Banach theorem is a favorite of almost every analyst. Its principal formulations are as a dominated extension theorem and as a separation theorem. In this paper we give an overview of the significance of the Hahn-Banach theorem to Analysis based on its historical background, formulation, implications, applications, significance and importance to Analysis and its contributions after discovery.

Keywords: Formulation of the theorem; Extension of linear functionals; Riesz’s contributions; Helly’s contributions; Hahn and Banach’s contributions; F.Murray contributions.

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International Journal of Modern Science and Technology

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ISSN 2456-0235