By Peano's space-filling curve, there exists a continuous map f: I -> I^2 whos image fills up the entire square I^2 (where I=[0, 1]). This can also be represented by gluing points of I together. Which points of I get glued together? I was looking at the proof of Peano's space-filling curve and I kind of get the idea it's all of them, although I'm having trouble justifying that. Would anyone like to shed some light on this?(adsbygoogle = window.adsbygoogle || []).push({});

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# Gluing points of [0, 1] to get [0, 1]^2

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