Pointwise convergence fails to be strict
Ján Borsík, Roman Frič · Czechoslovak Mathematical Journal · 1998
It is known that the ring $$B\left( \mathbb{R} \right)$$ of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring $$C\left( \mathbb{R} \right)$$ of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of $$C\left( \mathbb{R} \right)$$ . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of $$C\left( \mathbb{R} \right)$$ which differs from $$B\left( \mathbb{R} \right)$$ .