Matematicky ustav SAV, Gresakova 6, 040 01 Kosice, Slovakia, e-mail: borsik@linux1.saske.sk, fric@linux1.saske.sk
Abstract: It is known that the ring $B(\bb R)$ of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring $C(\bb R)$ of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of $C(\bb R)$. In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of $C(\bb R)$ which differs from $B(\bb R)$.
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