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In this paper, The combination of the structure of a vector space with the structure of a metric space naturally produces the structure of a normed space and a Banach space, i.e., of a complete linear normed space. The abstract definition of a linear normed space first appears around 1920 in the works of Stefan Banach (1892-1945), Hans Hahn (1879-1934) and Norbert Wiener (1894-1964) . In fact, it is in these years that the Polish school around Banach discovered the principles and laid thedoi:10.22214/ijraset.2019.7110 fatcat:f4wtkfwoxbb5njyyaygl5vpx7m