Are there $\pi$ -Dimension ? When I was thinking of dimensions such as about n-balls. I asked myself why isn't there a $\pi$-Ball. we always talk about n being a natural number. I know the illustration is difficult but the same applies for the 4th or 5th dimension. Thank you very much.
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9Consider this https://en.wikipedia.org/wiki/Fractal_dimension – Sonal_sqrt Jan 14 '20 at 14:50
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Ahh thank you. Didn’t know that, great! – Maths Jan 14 '20 at 14:52
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2@Sonal_sqrt So, what is a $\pi$ dimensional ball? – Berci Jan 14 '20 at 16:22
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2@Berci: That would be a metric space homeomorphic to, say, $B^3$, and having Hausdorff dimension equal to $\pi$. – Moishe Kohan Jan 14 '20 at 19:50
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2The "Canonical π dimensional space?" is essential this question, but not specifically about a ball. The answer there gives examples of $\pi$-dimensional (in the sense of fractal dimension aka Hausdorff dimension) objects. For some examples of fractal dimensions $\in[0,3]$ see this wikipedia article. – Vepir Jan 14 '20 at 19:53
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@Vepir Thank you! I was not aware of that answer on my old question. – Berci Jan 14 '20 at 20:04