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Abbott Dimension, Mathematics Inspired by Flatland

Siegert, Jeremy

The American mathematical monthly, 2024-02, Vol.131 (2), p.145-161 [Periódico revisado por pares]

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Título:
Abbott Dimension, Mathematics Inspired by Flatland
Autor: Siegert, Jeremy
Assuntos: Mathematical problems ; Metric space ; Metric system
É parte de: The American mathematical monthly, 2024-02, Vol.131 (2), p.145-161
Descrição: What is the "right way" to define dimension? Mathematicians working in the early and middle 20th-century formalized three intuitive definitions of dimension that all turned out to be equivalent on separable metric spaces. But were these definitions the "right" ones? What would it mean to have the "right" definition of dimension? In this paper we attempt to inspire thought about these questions by introducing Abbott dimension, a geometrically intuitive definition of dimension based on Edwin Abbott's 1884 novella Flatland. We show that while Abbott dimension has intuitive appeal, it does not always agree with the classical definitions of dimension on separable metric spaces.
Editor: Washington: Taylor & Francis Ltd
Idioma: Inglês

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