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PreprintCC BY-ND 4.0HAL

PROBLEM THEORY AND APPLICATION TO THE P VS NP PROBLEM

  • Theophilus Agama
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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.

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Cite

BibTeXRIS
BibTeX
@misc{agama2026problem,
  title = {{PROBLEM THEORY AND APPLICATION TO THE P VS NP PROBLEM}},
  author = {Theophilus Agama},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05763022v1},
  note = {CC BY-ND 4.0},
}
RIS
TY  - UNPB
TI  - PROBLEM THEORY AND APPLICATION TO THE P VS NP PROBLEM
AU  - Theophilus Agama
PY  - 2026
DA  - 2026/09/24
PB  - HAL
UR  - https://hal.science/hal-05763022v1
AB  - 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.
ER  -