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 sets.
@article{bwmeta1.element.bwnjournal-article-cmv86i2p203bwm,
author = {Marek Balcerzak and Udayan Darji},
title = {Some examples of true $F\_{$\sigma$$\delta$}$ sets},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {203-207},
zbl = {0961.03042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv86i2p203bwm}
}
Balcerzak, Marek; Darji, Udayan. Some examples of true $F_{σδ}$ sets. Colloquium Mathematicae, Tome 84/85 (2000) pp. 203-207. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv86i2p203bwm/
[000] [1] Z. Buczolich, Cantor type sets of positive measure and Lipschitz mappings, Real Anal. Exchange 17 (1991-92), 702-705. | Zbl 0858.28002
[001] [2] H. Hashimoto, On the *topology and its application, Fund. Math. 91 (1976), 5-10. | Zbl 0357.54002
[002] [3] D. Janković and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly 97 (1990), 295-310. | Zbl 0723.54005
[003] [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. | Zbl 0716.28003
[004] [5] A. S. Kechris, Classical Descriptive Set Theory, Springer, New York, 1994.
[005] [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. | Zbl 0633.03043
[006] [7] A. Louveau, σ-idéaux engendrés par des ensembles fermés et théorèmes d'approximation, ibid. 257 (1980), 143-169.
[007] [8] E. Matheron, How to recognize a true set, Fund. Math. 158 (1998), 181-194. | Zbl 0919.43003