{
  "abstract": "This paper introduces problem theory, a new framework for studying problem and solution spaces through the lens of point-set topology and abstract algebra. We define solution spaces as topological constructs induced by the assignment of solutions to problems and establish their fundamental properties. Key results include the identification of compactness and continuity conditions in solution spaces and their algebraic interpretations within module-theoretic settings. This theory bridges abstract algebra and topology, providing new insights into the interplay between algebraic structures and topological spaces. Potential applications and directions for future research are discussed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Theophilus Agama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bmvq2wkmvws8d.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "bmvq2wkmvws8d",
  "issns": [],
  "landing_url": "https://hal.science/hal-05763022v1",
  "language": "en",
  "licence": "CC-BY-ND-4.0",
  "licence_label": "CC BY-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05763022/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bmvq2wkmvws8d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "hal-05763022",
      "source": "hal",
      "url": "https://hal.science/hal-05763022v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "PROBLEM THEORY AND APPLICATION TO THE P VS NP PROBLEM",
  "title_text": "PROBLEM THEORY AND APPLICATION TO THE P VS NP PROBLEM",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:40Z",
  "url": "https://research.draconitic.com/paper/bmvq2wkmvws8d",
  "venue": "HAL",
  "versions": []
}