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Andrej Bauer

Are there space-filling curves, constructively? A blog post with pictures and animations. math.andrej.com/2024/01/30/spa

Image description: David Hilbert's original paper on space-filling curves contained three pictures, shown here, demonstrating how a space-filling curve is constructed in stages: a curve is made of four parts, each parts is replaced by a small copy of the the previous stage to obtain the next one.
The King

@andrejbauer you can prove theorem 2 without choice for the Cauchy reals. Thus, countable choice implies it for the Dedekind reals.

Feb 09, 2024, 08:19 PM·Public·Web
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