I might be missing something obvious here, but my understanding is that nobody currently knows whether the boundary of the Mandelbrot set is a Jordan curve because otherwise we would know that the Mandelbrot set were path-connected which according to Wikipedia we don't. But what about the other way around? Do we maybe know that the boundary is not a Jordan curve? Or even that it's not continuous?
2025-01-13 08:48:57.1736758137
Is it known whether the boundary of the Mandelbrot set is not continuous?
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