2 

     2 

     3 \section{Comparing definitions of $A_\infty$ algebras}

     3 \section{Comparing definitions of $A_\infty$ algebras}

     4 \label{sec:comparing-A-infty}

     4 \label{sec:comparing-A-infty}

     5 In this section, we make contact between the usual definition of an $A_\infty$ algebra and our definition of a topological $A_\infty$ algebra, from Definition \ref{defn:topological-Ainfty-category}.

     5 In this section, we make contact between the usual definition of an $A_\infty$ algebra and our definition of a topological $A_\infty$ algebra, from Definition \ref{defn:topological-Ainfty-category}.

     6 

     6