Sequential convergence in $C_p(X)$
Fremlin, David H.
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 371-382 / Harvested from Czech Digital Mathematics Library
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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 $C_p(X)$.

Publié le : 1994-01-01
Classification:  54A20,  54C30,  54C35 
@article{118677,
     author = {David H. Fremlin},
     title = {Sequential convergence in $C\_p(X)$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {371-382},
     zbl = {0827.54002},
     mrnumber = {1286585},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118677}
}

Fremlin, David H. Sequential convergence in $C_p(X)$. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 371-382. http://gdmltest.u-ga.fr/item/118677/

Bourgain J. New classes of $\Cal L_p$ spaces, Springer, 1981 (Lecture Notes in Mathematics 889). | MR 0639014

Day M.M. Normed Spaces, Springer, 1962. | Zbl 0316.46010

Van Douwen E.K. The integers and topology, pp. 111-167 in 11. | MR 0776622 | Zbl 0561.54004

Dugundji J. An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367. (1951) | MR 0044116 | Zbl 0043.38105

Engelking R. General Topology, Heldermann, 1989. | MR 1039321 | Zbl 0684.54001

Fremlin D.H. Supplement to ``Convergent sequences in $C_p(X)$'', University of Essex Mathematics Department Research Report 92-14.

Gerlits J.; Nagy Z. Some properties of $C(X)$, Topology Appl. 14 (1982), 151-161. (1982) | MR 0667661 | Zbl 0503.54020

Jameson G.J.O. Topology and Normed Spaces, Chapman & Hall, 1974. | MR 0463890 | Zbl 0285.46002

Kechris A.S.; Louveau A. Descriptive Set Theory and Sets of Uniqueness, Cambridge U.P., 1987. | MR 0953784

Köthe G. Topologische Lineare Räume, Springer, 1960. | MR 0130551

Kunen K.; Vaughan J.E. Handbook of Set-Theoretic Topology, North-Holland, 1984. | MR 0776619 | Zbl 0674.54001

Kuratowski K. Topology, vol I., Academic, 1966. | MR 0217751 | Zbl 0849.01044

Miller A.W. On the length of Borel hierarchies, Ann. Math. Logic 16 (1979), 233-267. (1979) | MR 0548475 | Zbl 0415.03038