10:11 AM
These two questions seem to be duplicates. (At least to me.)
2

Is there a simple geometric proof that there exists a continuous bijective function between a square and its side? And is there some explicit continuous function or formula $f^1(z)\mapsto (x,y)$ and $f(x,y)\mapsto z$, with $(x,y) \in [0,1]\times[0,1]$ and $z \in [0,1]$? And is there a constru...

4

Is there a continuous bijection from $[0,1]$ onto $[0,1] \times [0,1]$? That is with $I=[0,1]$ and $S=[0,1] \times [0,1]$, is there a continuous bijection $$f: I \to S?$$ I know there is a continuous bijection $g:C \to I$ from the Cantor set $C$ to $[0,1]$. The square $S$ is compact so there i...

However, the newer question seems to be better formulated and it has more answers. So perhaps it would be better to close the older one as a duplicate of the newer?

2 hours later…
11:47 AM
The older question already has 3 close votes, two more are missing.

12:08 PM
The question is closed now.