点维理论（上）：点扩展盒维
Point-Dimension Theory (Part I): The Point-Extended Box Dimension
摘要：
这篇文章是一个更大的研究项目，致力于纯，应用和维度理论的哲学方面的介绍性工作。它涉及到一个新的方法对交替的维度理论基础：点维理论。为此目的，对这一概念和相关概念的历史研究，结合批判性分析和哲学发展证明是必要的。因此，我们的主要目标是挑战传统的零维分配给点。这种重新思考使我们能够提出两种新的方式来构思维度的概念，它们是同一枚硬币的两面。首先，作为一个组织;因此，我们认为存在着一种基本粒子，它赋予物体和时空以维度。这种粒子存在的想法可能被当作一种投影，以创造一种统一量子力学和爱因斯坦广义相对论的替代方法。其次，与玻尔兹曼熵和香农熵有关，维数本质上是集合熵之间的比较。因此，我们从点出发，并成功地构建了一个点维概念，使我们能够在许多方向上扩展盒维原理。更确切地说，我们在拓扑向量空间的大框架中引入了点扩展盒维数的概念，将其从度量的概念中解放出来。这个一般的设定使我们能够处理有限、无限和不可见维的情况。我们的研究项目的第一部分主要集中在一般性质，特别是面向建立一个有充分依据的框架无限维。其中，一个前景是测试使用其他类型的空间作为量子力学背景的可能性，而不是将其限制在唯一的希尔伯特框架中。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
