dorsal/arxiv
View SchemaScanning the structure of ill-known spaces: Part 1. Founding principles about mathematical constitution of space
| Authors | Michel Bounias, Volodymyr Krasnoholovets |
|---|---|
| Categories | |
| ArXiv ID | physics/0211096 |
| URL | https://arxiv.org/abs/physics/0211096 |
| Journal | Kybernetes: The International Journal of Systems & Cybernetics, Vol. 32, No. 7/8, pp. 945-975 (2003) |
Abstract
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.
{
"annotation_id": "c11ddc1f-d410-4624-9fb8-ed703b1f05e8",
"date_created": "2026-03-02T18:00:43.521000Z",
"date_modified": "2026-03-02T18:00:43.521000Z",
"file_hash": "b20d44f4abc5b9b82c42664a8e072da1f6d932c4fa6dea1ffa0765b7bb81798b",
"private": false,
"record": {
"abstract": "Necessary and sufficient conditions allowing a previously unknown space to be\nexplored through scanning operators are reexamined with respect to measure\ntheory. Generalized conceptions of distances and dimensionality evaluation are\nproposed, together with their conditions of validity and range of application\nto topological spaces. The existence of a Boolean lattice with fractal\nproperties originating from nonwellfounded properties of the empty set is\ndemonstrated. This lattice provides a substrate with both discrete and\ncontinuous properties, from which existence of physical universes can be\nproved, up to the function of conscious perception. Spacetime emerges as an\nordered sequence of mappings of closed 3-D Ponicare sections of a topological\n4-space provided by the lattice. The possibility of existence of spaces with\nfuzzy dimension or with adjoined parts with decreasing dimensions is raised,\ntogether with possible tools for their study. The work provides the\nintroductory foundations supporting a new theory of space whose physical\npredictions (suppressing the opposition of quantum and relativistic approaches)\nand experimental proofs are presented in details in Parts 2 and 3 of the study.",
"arxiv_id": "physics/0211096",
"authors": [
"Michel Bounias",
"Volodymyr Krasnoholovets"
],
"categories": [
"physics.gen-ph"
],
"journal_ref": "Kybernetes: The International Journal of Systems \u0026 Cybernetics,\n Vol. 32, No. 7/8, pp. 945-975 (2003)",
"title": "Scanning the structure of ill-known spaces: Part 1. Founding principles about mathematical constitution of space",
"url": "https://arxiv.org/abs/physics/0211096"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "5015d210-5319-4ace-90c6-8448ded8c08f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}