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-\begin{omgroup}[id=sec.contfuncs]{Continuous Functions}
-\begin{module}[id=continuous]
-\importmodule[load=\backmods{functions}]{functions}
-\importmodule[load=\backmods{reals}]{reals}
-\symdef{continuousfunctions}[2]{\mathcal{C}^0(#1,#2)}
-\abbrdef{ContRR}[2]{\continuousfunctions\RealNumbers\RealNumbers}
-\begin{definition}[for=continuousfunctions]
- A function $\fun{f}\RealNumbers\RealNumbers$ is called {\defi{continuous}} at
- $\inset{x}\RealNumbers$, iff for all $\epsilon>0$ there is a $\delta>0$, such that
- $\absval{f(x)-f(y)}<\epsilon$ for all $\absval{x-y}<\delta$. It is called
- {\defii{continuous}{on}} a set $\sseteq{S}\RealNumbers$, iff is is continous at all
- $\inset{x}S$, the set of all such functions is denoted with $\continuousfunctions{S}T$,
- if $\sseteq{f(S)}T$.
-\end{definition}
-\end{module}
-\end{omgroup}
-%%% Local Variables:
-%%% mode: LaTeX
-%%% TeX-master: "paper"
-%%% End: