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authorKarl Berry <karl@freefriends.org>2012-03-30 23:23:02 +0000
committerKarl Berry <karl@freefriends.org>2012-03-30 23:23:02 +0000
commit849996eca72af498b48b10fbea7f14c4b9d21b8f (patch)
tree2d40d42dfc9fc0b0622212cc220868f98345305f /Master/texmf-dist/doc/latex/stex/example/paper/continuous.tex
parentd82e1c23973fd0271f93686f487bd1cee8dcd947 (diff)
restore stex (ca. 28jan12)
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+\begin{omgroup}[id=sec.contfuncs]{Continuous Functions}
+\begin{module}[id=continuous]
+\importmodule[\backmods{functions}]{functions}
+\importmodule[\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: