Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
sequential convergence; $C_p(X)$
sequential convergence; $C_p(X)$
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 $C_p(X)$.
References:
[1] Bourgain J.: New classes of $\Cal L_p$ spaces. Springer, 1981 (Lecture Notes in Mathematics 889). MR 0639014
[2] Day M.M.: Normed Spaces. Springer, 1962. Zbl 0316.46010
[3] van Douwen E.K.: The integers and topology. pp. 111-167 in 11. MR 0776622 | Zbl 0561.54004
[4] Dugundji J.: An extension of Tietze's theorem. Pacific J. Math. 1 (1951), 353-367. MR 0044116 | Zbl 0043.38105
[5] Engelking R.: General Topology. Heldermann, 1989. MR 1039321 | Zbl 0684.54001
[6] Fremlin D.H.: Supplement to ``Convergent sequences in $C_p(X)$''. University of Essex Mathematics Department Research Report 92-14.
[7] Gerlits J., Nagy Z.: Some properties of $C(X)$. Topology Appl. 14 (1982), 151-161. MR 0667661 | Zbl 0503.54020
[8] Jameson G.J.O.: Topology and Normed Spaces. Chapman & Hall, 1974. MR 0463890 | Zbl 0285.46002
[9] Kechris A.S., Louveau A.: Descriptive Set Theory and Sets of Uniqueness. Cambridge U.P., 1987. MR 0953784
[10] Köthe G.: Topologische Lineare Räume. Springer, 1960. MR 0130551
[11] Kunen K., Vaughan J.E.: Handbook of Set-Theoretic Topology. North-Holland, 1984. MR 0776619 | Zbl 0674.54001
[12] Kuratowski K.: Topology. vol I., Academic, 1966. MR 0217751 | Zbl 0849.01044
[13] Miller A.W.: On the length of Borel hierarchies. Ann. Math. Logic 16 (1979), 233-267. MR 0548475 | Zbl 0415.03038
Search
Partner of
