  The notion of strict closedness of rings was given by J. Lipman in connection
with a conjecture of O. Zariski. The present purpose is to give a practical
method of construction of strictly closed rings. It is also shown that the
Stanley-Reisner rings of simplicial complexes (resp. $F$-pure rings satisfying
the condition $(S_2)$ of Serre) are strictly closed (resp. weakly Arf) rings.
