Pointwise convergence fails to be strict

Ján Borsík; Roman Frič

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 2, page 313-320
  • ISSN: 0011-4642

Abstract

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It is known that the ring B ( ℝ ) of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring C ( ℝ ) of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of C ( ℝ ) . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of C ( ℝ ) which differs from B ( ℝ ) .

How to cite

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Borsík, Ján, and Frič, Roman. "Pointwise convergence fails to be strict." Czechoslovak Mathematical Journal 48.2 (1998): 313-320. <http://eudml.org/doc/30420>.

@article{Borsík1998,
abstract = {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 $B(\mathbb \{R\})$.},
author = {Borsík, Ján, Frič, Roman},
journal = {Czechoslovak Mathematical Journal},
keywords = {sequential completion; Baire functions; pointwise convergence; categorical ring completion},
language = {eng},
number = {2},
pages = {313-320},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Pointwise convergence fails to be strict},
url = {http://eudml.org/doc/30420},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Borsík, Ján
AU - Frič, Roman
TI - Pointwise convergence fails to be strict
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 2
SP - 313
EP - 320
AB - 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 $B(\mathbb {R})$.
LA - eng
KW - sequential completion; Baire functions; pointwise convergence; categorical ring completion
UR - http://eudml.org/doc/30420
ER -

References

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  3. Coarse sequential convergence in groups, etc, Czechoslovak Math. J. 40 (115) (1990), 459–467. (1990) MR1065025
  4. Strict completions of L 0 * -groups, Czechoslovak Math. J. 42 (117) (1992), 589–598. (1992) MR1182190
  5. Category Theory, 2nd edition, Heldermann Verlag, Berlin, 1976. (1976) MR2377903
  6. Baire 1 functions, Real Analysis Exch. 9 (1983/84), 15–28. (1983/84) 
  7. On completions of convergence commutative groups, In: General Topology and its Relations to Modern Analysis and Algebra III (Proc. Third Prague Topological Sympos., 1971), Academia, Praha, 1972, pp. 335–340. (1972) MR0365451
  8. Strictness of L 0 -ring completions, Tatra Mountains Math. Publ. 5 (1995), 169–175. (1995) MR1384806

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