扫描未知空间的结构：第1部分。空间数学构成的基本原理
Scanning the structure of ill-known spaces: Part 1. Founding principles about mathematical constitution of space
摘要：
必要和充分条件允许一个以前未知的空间进行探索，通过扫描运营商重新审查与测量理论。提出了距离和维数估计的广义概念，并给出了它们在拓扑空间中的有效性条件和应用范围。证明了一个具有分形性质的布尔格的存在性，该分形性质源于空集的非良基性质。这种晶格提供了一个具有离散和连续性质的基底，从中可以证明物理宇宙的存在，直到意识感知的功能。时空是由格点提供的拓扑四维空间的封闭三维庞加莱截面映射的有序序列。提出了具有模糊维数或具有降维邻接部分的空间存在的可能性，以及研究它们的可能工具。这项工作提供了一个新的空间理论的基础，其物理预测（抑制量子和相对论方法的对立）和实验证明在研究的第2部分和第3部分中详细介绍。
英文摘要：
Necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Generalized conceptions of distances and dimensionality evaluation are proposed, together with their conditions of validity and range of application to topological spaces. The existence of a Boolean lattice with fractal properties originating from nonwellfounded properties of the empty set is demonstrated. This lattice provides a substrate with both discrete and continuous properties, from which existence of physical universes can be proved, up to the function of conscious perception. Spacetime emerges as an ordered sequence of mappings of closed 3-D Ponicare sections of a topological 4-space provided by the lattice. The possibility of existence of spaces with fuzzy dimension or with adjoined parts with decreasing dimensions is raised, together with possible tools for their study. The work provides the introductory foundations supporting a new theory of space whose physical predictions (suppressing the opposition of quantum and relativistic approaches) and experimental proofs are presented in details in Parts 2 and 3 of the study.
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