On a Classical Review of the Fundamental Hahn-Banach Extension Result in Polynomial and Dirichlet Pr

The Hahn-Banach theorem is discussed as an efficient development for functional extension in Banach spaces prior to other later breakthroughs in topology and functional analysis. The Hahn-Banach result essentially depicts the extent to which the values of a linear functional could be pre-assigned, and in this work, one considers a mathematical object specified on a subset of a given set X in a manner in which features of the objects are retained and extended, as described in section one below. The principles of the Hahn-Banach results as accurately evaluated as results and sub results are covered in section two. These served as the foundation for this study, with several applications covered in detail in section three.

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