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Homotopy theory, homological algebra, algebraic treatments of manifolds.

2 votes
0 answers
85 views

$n$-point map $S$ from $k$-manifold $X$ to $\mathbb{R}^k$

It is known that for every continuous map $M:S^1\to \mathbb{R}$ there are infinitely many double points. Also by the Borsuk-Ulam theorem, this is true for each continuous map $N:S^n\to \mathbb{R}^n$, …
MasM's user avatar
  • 289
4 votes
0 answers
428 views

On some characteristics of continuous maps $S^n \to \mathbb{R}^n$

I've asked this question about two month ago in math exchange but there were no answer to it. Any information or paper relating to this question is appreciated. By the Borsuk-Ulam theorem we know tha …
MasM's user avatar
  • 289
5 votes
3 answers
471 views

Is there a dense subset on closed Jordan curve $C$ which its points make intersections under...

Is it true that for any given closed Jordan curve of $C \subset \mathbb{R}^2$ there is a dense subset $A$ such that for every point $p\in A$ we have the following property: If we rotate $C$ around $p …
MasM's user avatar
  • 289
1 vote
Accepted

Is there a dense subset on closed Jordan curve $C$ which its points make intersections under...

Thanks for the efforts have done on this problem specially by @erz ,but It seems that Mark J.Nielsen have solved this problem here (that I have found it recently), while he was proving this theorem a …