Geodesic
Pointwise convergence fails to be strict
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 2, pp. 313-320 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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It is known that the ring $B(\mathbb R)$ of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring $C(\mathbb R)$ of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of $C(\mathbb R)$. In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of $C(\mathbb R)$ which differs from $B(\mathbb R)$.
It is known that the ring $B(\mathbb R)$ of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring $C(\mathbb R)$ of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of $C(\mathbb R)$. In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of $C(\mathbb R)$ which differs from $B(\mathbb R)$.
Classification : 46E25, 54A05, 54C30, 54C35 
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Borsík, Ján; Frič, Roman. Pointwise convergence fails to be strict. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 2, pp. 313-320. http://geodesic.mathdoc.fr/item/CMJ_1998_48_2_a7/

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