1 %!TEX root = ../../blob1.tex

     1 %!TEX root = ../../blob1.tex

     2 

     2 

     3 \section{Adapting families of maps to open covers}  \label{sec:localising}

     3 \section{Adapting families of maps to open covers}  \label{sec:localising}

     4 

     4 

     5 

     7 

     6 Let $X$ and $T$ be topological spaces, with $X$ compact.

     8 Let $X$ and $T$ be topological spaces, with $X$ compact.

     7 Let $\cU = \{U_\alpha\}$ be an open cover of $X$ which affords a partition of

     9 Let $\cU = \{U_\alpha\}$ be an open cover of $X$ which affords a partition of

     8 unity $\{r_\alpha\}$.

    10 unity $\{r_\alpha\}$.

     9 (That is, $r_\alpha : X \to [0,1]$; $r_\alpha(x) = 0$ if $x\notin U_\alpha$;

    11 (That is, $r_\alpha : X \to [0,1]$; $r_\alpha(x) = 0$ if $x\notin U_\alpha$;