| Title:
|
Pointwise convergence fails to be strict (English) |
| Author:
|
Borsík, Ján |
| Author:
|
Frič, Roman |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
313-320 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $B(\mathbb R)$. (English) |
| MSC:
|
46E25 |
| MSC:
|
54A05 |
| MSC:
|
54C30 |
| MSC:
|
54C35 |
| idZBL:
|
Zbl 0954.46015 |
| idMR:
|
MR1624327 |
| . |
| Date available:
|
2009-09-24T10:13:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127418 |
| . |
| Reference:
|
[FKE] Frič, R. and Kent, D. C.: Regularity and extension of maps.Math. Slovaca 42 (1992), 349–357. MR 1182965 |
| Reference:
|
[FKO] Frič, R. and Koutník, V.: Completions for subcategories of convergence rings.In: Categorical Topology and its Relations to Modern Analysis, Algebra and Combinatorics, World Scientific Publishing Co., Singapore, 1989, pp. 195–207. MR 1047901 |
| Reference:
|
[FZE] Frič, R. and Zanolin, F.: Coarse sequential convergence in groups, etc.Czechoslovak Math. J. 40 (115) (1990), 459–467. MR 1065025 |
| Reference:
|
[FZS] Frič, R. and Zanolin, F.: Strict completions of $L _0^*$-groups.Czechoslovak Math. J. 42 (117) (1992), 589–598. MR 1182190 |
| Reference:
|
[HES] Herrlich, H. and Strecker, G. E.: Category Theory.2nd edition, Heldermann Verlag, Berlin, 1976. MR 2377903 |
| Reference:
|
[LAC] Laczkovich, M.: Baire 1 functions.Real Analysis Exch. 9 (1983/84), 15–28. |
| Reference:
|
[NOV] Novák, J.: 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. MR 0365451 |
| Reference:
|
[PAU] Paulík, L.: Strictness of $L_0$-ring completions.Tatra Mountains Math. Publ. 5 (1995), 169–175. MR 1384806 |
| . |
