# On the use of semi-closed sets and functions in convex analysis

The main aim of this short note is to show that the sub\-differentiability and duality results established by Laghdir (2005), Laghdir and Benabbou (2007), and Alimohammady \emph{et al.}\ (2011), stated in Fréchet spaces, are consequences of the corresponding known results using Moreau--Rockafellar type conditions.