Sequential convergence in C p ( X )

David H. Fremlin

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 2, page 371-382
  • ISSN: 0010-2628

Abstract

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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 ) .

How to cite

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Fremlin, David H.. "Sequential convergence in $C_p(X)$." Commentationes Mathematicae Universitatis Carolinae 35.2 (1994): 371-382. <http://eudml.org/doc/247575>.

@article{Fremlin1994,
abstract = {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 $C_p(X)$.},
author = {Fremlin, David H.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sequential convergence; $C_p(X)$; sequential convergence; sequential closure of sets; normed spaces},
language = {eng},
number = {2},
pages = {371-382},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Sequential convergence in $C_p(X)$},
url = {http://eudml.org/doc/247575},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Fremlin, David H.
TI - Sequential convergence in $C_p(X)$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 2
SP - 371
EP - 382
AB - 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 $C_p(X)$.
LA - eng
KW - sequential convergence; $C_p(X)$; sequential convergence; sequential closure of sets; normed spaces
UR - http://eudml.org/doc/247575
ER -

References

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  1. Bourgain J., New classes of ℒ p spaces, Springer, 1981 (Lecture Notes in Mathematics 889). MR0639014
  2. Day M.M., Normed Spaces, Springer, 1962. Zbl0316.46010
  3. van Douwen E.K., The integers and topology, pp. 111-167 in 11. Zbl0561.54004MR0776622
  4. Dugundji J., An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367. (1951) Zbl0043.38105MR0044116
  5. Engelking R., General Topology, Heldermann, 1989. Zbl0684.54001MR1039321
  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. (1982) Zbl0503.54020MR0667661
  8. Jameson G.J.O., Topology and Normed Spaces, Chapman & Hall, 1974. Zbl0285.46002MR0463890
  9. Kechris A.S., Louveau A., Descriptive Set Theory and Sets of Uniqueness, Cambridge U.P., 1987. MR0953784
  10. Köthe G., Topologische Lineare Räume, Springer, 1960. MR0130551
  11. Kunen K., Vaughan J.E., Handbook of Set-Theoretic Topology, North-Holland, 1984. Zbl0674.54001MR0776619
  12. Kuratowski K., Topology, vol I., Academic, 1966. Zbl0849.01044MR0217751
  13. Miller A.W., On the length of Borel hierarchies, Ann. Math. Logic 16 (1979), 233-267. (1979) Zbl0415.03038MR0548475

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