| Title:
|
Sequential convergence in $C_p(X)$ (English) |
| Author:
|
Fremlin, D. H. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
371-382 |
| . |
| Category:
|
math |
| . |
| Summary:
|
I discuss the number of iterations of the elementary sequential closure operation required to achieve the full sequential closure of a set in spaces of the form $C_p(X)$. (English) |
| Keyword:
|
sequential convergence |
| Keyword:
|
$C_p(X)$ |
| MSC:
|
54A20 |
| MSC:
|
54C30 |
| MSC:
|
54C35 |
| idZBL:
|
Zbl 0827.54002 |
| idMR:
|
MR1286585 |
| . |
| Date available:
|
2009-01-08T18:11:48Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118677 |
| . |
| Reference:
|
[1] Bourgain J.: New classes of $\Cal L_p$ spaces.Springer, 1981 (Lecture Notes in Mathematics 889). MR 0639014 |
| Reference:
|
[2] Day M.M.: Normed Spaces.Springer, 1962. Zbl 0316.46010 |
| Reference:
|
[3] van Douwen E.K.: The integers and topology.pp. 111-167 in 11. Zbl 0561.54004, MR 0776622 |
| Reference:
|
[4] Dugundji J.: An extension of Tietze's theorem.Pacific J. Math. 1 (1951), 353-367. Zbl 0043.38105, MR 0044116 |
| Reference:
|
[5] Engelking R.: General Topology.Heldermann, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[6] Fremlin D.H.: Supplement to ``Convergent sequences in $C_p(X)$''.University of Essex Mathematics Department Research Report 92-14. |
| Reference:
|
[7] Gerlits J., Nagy Z.: Some properties of $C(X)$.Topology Appl. 14 (1982), 151-161. Zbl 0503.54020, MR 0667661 |
| Reference:
|
[8] Jameson G.J.O.: Topology and Normed Spaces.Chapman & Hall, 1974. Zbl 0285.46002, MR 0463890 |
| Reference:
|
[9] Kechris A.S., Louveau A.: Descriptive Set Theory and Sets of Uniqueness.Cambridge U.P., 1987. MR 0953784 |
| Reference:
|
[10] Köthe G.: Topologische Lineare Räume.Springer, 1960. MR 0130551 |
| Reference:
|
[11] Kunen K., Vaughan J.E.: Handbook of Set-Theoretic Topology.North-Holland, 1984. Zbl 0674.54001, MR 0776619 |
| Reference:
|
[12] Kuratowski K.: Topology.vol I., Academic, 1966. Zbl 0849.01044, MR 0217751 |
| Reference:
|
[13] Miller A.W.: On the length of Borel hierarchies.Ann. Math. Logic 16 (1979), 233-267. Zbl 0415.03038, MR 0548475 |
| . |
