  This article is an introductory work to a larger research project devoted to
pure, applied and philosophical aspects of dimension theory. It concerns a
novel approach toward an alternate dimension theory foundation: the
point-dimension theory. For this purpose, historical research on this notion
and related concepts, combined with critical analysis and philosophical
development proved necessary. Hence, our main objective is to challenge the
conventional zero dimension assigned to the point. This reconsideration allows
us to propose two new ways of conceiving the notion of dimension, which are the
two sides of the same coin. First as an organization; accordingly, we suggest
the existence of the Dimensionad, an elementary particle conferring dimension
to objects and space-time. The idea of the existence of this particle could
possibly adopted as a projection to create an alternative way to unify quantum
mechanics and Einstein's general relativity. Secondly, in connection with
Boltzmann and Shannon entropies, dimension appears essentially as a comparison
between entropies of sets. Thus, we started from the point and succeeded in
constructing a point-dimension notion allowing us to extend the principle of
box dimension in many directions. More precisely, we introduce the notion of
point-extended box dimension in the large framework of topological vector
spaces, freeing it from the notion of metric. This general setting permits us
to treat the case of finite, infinite and invisible dimensions. This first part
of our research project focuses essentially on general properties and is
particularly oriented towards establishing a well founded framework for
infinite dimension. Among others, one prospect is to test the possibility of
using other types of spaces as a setting for quantum mechanics, instead of
limiting it to the exclusive Hilbertian framework.
