2
$\begingroup$

Let $X$ be the set of continuous, injective functions from $\mathbb{R}^n$ to $\mathbb{R}^n$ with dense image; and equip $X$ with the (relative) compact-open topology. What is known about this space?

In particular, are all such maps cell-like (cellular)?

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ Just looking at what you link, it seems to suggest that if it were cell like such a thing would be a limit of homeomorphisms which obviously can’t happen if the dimensions are different. $\endgroup$
    – Connor Malin
    Commented Nov 6, 2020 at 16:32
  • $\begingroup$ @ConnorMalin Yes sorry, $n$ is replaced with $m$. Thanks for pointing that out. $\endgroup$
    – ABIM
    Commented Nov 6, 2020 at 16:40
  • 1
    $\begingroup$ An injective map is cellular if and only if it is bijective. $\endgroup$
    – skupers
    Commented Nov 6, 2020 at 16:57

0

Reset to default

You must log in to answer this question.