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Updated: May 4, 2026

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New 5-adic Cantor sets and fractal string.

Ashish Kumar1, Mamta Rani2, Renu Chugh1

  • 1Department of Mathematics, Maharshi Dayanand University, Rohtak, 124001 Haryana India.

Springerplus
|January 4, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces the 5-adic Cantor one-fifth set, a novel fractal string. It also explores the set's potential applications within string theory.

Keywords:
11E2026A3026A8026E3028A1228A8028E305-adic Cantor one-fifth setCantor one-fifth setFractal stringIterated function system (IFS)p-adic integers

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Area of Science:

  • Set Theory
  • Fractal Geometry
  • String Theory

Background:

  • George Cantor's foundational work in set theory (1879-1884) introduced concepts like the Cantor ternary set.
  • The Cantor ternary set is a classical example of a fractal, demonstrating self-similarity.

Purpose of the Study:

  • To introduce the 5-adic Cantor one-fifth set as a new example of a fractal string.
  • To investigate the potential applications of this novel fractal set in string theory.

Main Methods:

  • Introduction of the 5-adic Cantor one-fifth set.
  • Exploration of its properties as a fractal string.
  • Analysis of its relevance and potential uses in string theory.

Main Results:

  • The 5-adic Cantor one-fifth set is presented as a fractal string.
  • Initial studies suggest potential applications in string theory.

Conclusions:

  • The 5-adic Cantor one-fifth set expands the family of fractal strings.
  • Further research is warranted to fully explore its implications in string theory.