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This article is an introductory work to a larger research project devoted topure, applied and philosophical aspects of dimension theory. It concerns anovel approach toward an alternate dimension theory foundation: thepoint-dimension theory. For this purpose, historical research on this notionand related concepts, combined with critical analysis and philosophicaldevelopment proved necessary. Hence, our main objective is to challenge theconventional zero dimension assigned to the point. This reconsideration allowsus to propose two new ways of conceiving the notion of dimension, which are thetwo sides of the same coin. First as an organization; accordingly, we suggestthe existence of the Dimensionad, an elementary particle conferring dimensionto objects and space-time. The idea of the existence of this particle couldpossibly adopted as a projection to create an alternative way to unify quantummechanics and Einstein's general relativity. Secondly, in connection withBoltzmann and Shannon entropies, dimension appears essentially as a comparisonbetween entropies of sets. Thus, we started from the point and succeeded inconstructing a point-dimension notion allowing us to extend the principle ofbox dimension in many directions. More precisely, we introduce the notion ofpoint-extended box dimension in the large framework of topological vectorspaces, freeing it from the notion of metric. This general setting permits usto treat the case of finite, infinite and invisible dimensions. This first partof our research project focuses essentially on general properties and isparticularly oriented towards establishing a well founded framework forinfinite dimension. Among others, one prospect is to test the possibility ofusing other types of spaces as a setting for quantum mechanics, instead oflimiting it to the exclusive Hilbertian framework.

Point-Dimension Theory (Part I): The Point-Extended Box Dimension