4
$\begingroup$

$X$ is a topological space that is contractible and compact. Show that if $U$ is an open set in $X$ containing $x_0$ then there exists $t_0<1$ so that $H(x,t)∈U$, for all $x∈X$, and all $t_0≤t≤1$. Here $H(x,t)$ is the homotopy from the identity map to the constant map.

  • 2
    The set $H^{-1}[U]$ is an open neighbourhood of $X\times\{1\}$. What can you conclude?2012-11-26

0 Answers 0