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Constructing a Linearly Ordered Topological Space from a Fractal Structure: A Probabilistic Approach

Author

Listed:
  • José Fulgencio Gálvez-Rodríguez

    (Department of Mathematics, Universidad de Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

  • Miguel Ángel Sánchez-Granero

    (Department of Mathematics, Universidad de Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

Abstract

Recent studies have shown that it is possible to construct a probability measure from a fractal structure defined on a space. On the other hand, a theory on cumulative distribution functions from an order on a separable linearly ordered topological space has been developed. In this paper, we show how to define a linear order on a space with a fractal structure, so that these two theories can be used interchangeably in both topological contexts.

Suggested Citation

  • José Fulgencio Gálvez-Rodríguez & Miguel Ángel Sánchez-Granero, 2022. "Constructing a Linearly Ordered Topological Space from a Fractal Structure: A Probabilistic Approach," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4518-:d:988543
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    References listed on IDEAS

    as
    1. Georgios Souliotis & Yousif Alanazi & Basil Papadopoulos, 2022. "Construction of Fuzzy Numbers via Cumulative Distribution Function," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
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