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### Is there a line homomorphism to a disk? [duplicate]

This is a question from an interview. I am confused about this problem. I said yes in that interview because I remember something about Hilbert curve(I mean, is there a line that can fill a square ...
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### Probability that 3 points in a plane form a triangle

This question was asked in a test and I got it right. The answer key gives $\frac12$. Problem: If 3 distinct points are chosen on a plane, find the probability that they form a triangle. Attempt 1:...
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### Is there a continuous bijection from $\mathbb{R}$ to $\mathbb{R}^2$

I need a hint. The problem is: is there a continuous bijection from $\mathbb{R}$ to $\mathbb{R}^2$ I'm pretty sure that there aren't any, but so far I couldn't find the proof. My best idea so far is ...