Some examples of true F σ δ sets

Marek Balcerzak; Udayan Darji

Colloquium Mathematicae (2000)

  • Volume: 86, Issue: 2, page 203-207
  • ISSN: 0010-1354

Abstract

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Let K(X) be the hyperspace of a compact metric space endowed with the Hausdorff metric. We give a general theorem showing that certain subsets of K(X) are true F σ δ sets.

How to cite

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Balcerzak, Marek, and Darji, Udayan. "Some examples of true $F_{σδ}$ sets." Colloquium Mathematicae 86.2 (2000): 203-207. <http://eudml.org/doc/210850>.

@article{Balcerzak2000,
abstract = {Let K(X) be the hyperspace of a compact metric space endowed with the Hausdorff metric. We give a general theorem showing that certain subsets of K(X) are true $F_\{σδ\}$ sets.},
author = {Balcerzak, Marek, Darji, Udayan},
journal = {Colloquium Mathematicae},
keywords = {Borel set; hyperspace; compact metric space; Borel sets},
language = {eng},
number = {2},
pages = {203-207},
title = {Some examples of true $F_\{σδ\}$ sets},
url = {http://eudml.org/doc/210850},
volume = {86},
year = {2000},
}

TY - JOUR
AU - Balcerzak, Marek
AU - Darji, Udayan
TI - Some examples of true $F_{σδ}$ sets
JO - Colloquium Mathematicae
PY - 2000
VL - 86
IS - 2
SP - 203
EP - 207
AB - Let K(X) be the hyperspace of a compact metric space endowed with the Hausdorff metric. We give a general theorem showing that certain subsets of K(X) are true $F_{σδ}$ sets.
LA - eng
KW - Borel set; hyperspace; compact metric space; Borel sets
UR - http://eudml.org/doc/210850
ER -

References

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  1. [1] Z. Buczolich, Cantor type sets of positive measure and Lipschitz mappings, Real Anal. Exchange 17 (1991-92), 702-705. Zbl0858.28002
  2. [2] H. Hashimoto, On the *topology and its application, Fund. Math. 91 (1976), 5-10. Zbl0357.54002
  3. [3] D. Janković and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly 97 (1990), 295-310. Zbl0723.54005
  4. [4] W. Just and C. Laflamme, Classifying sets of measure zero with respect to their open covers, Trans. Amer. Math. Soc. 321 (1990), 621-645. Zbl0716.28003
  5. [5] A. S. Kechris, Classical Descriptive Set Theory, Springer, New York, 1994. 
  6. [6] A. S. Kechris, A. Louveau and H. Woodin, The structure of σ-ideals of compact sets, Trans. Amer. Math. Soc. 301 (1987), 263-288. Zbl0633.03043
  7. [7] A. Louveau, σ-idéaux engendrés par des ensembles fermés et théorèmes d'approximation, ibid. 257 (1980), 143-169. 
  8. [8] E. Matheron, How to recognize a true Σ 3 0 set, Fund. Math. 158 (1998), 181-194. Zbl0919.43003

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