The Lindelöf property and σ-fragmentability

B. Cascales, and I. Namioka. "The Lindelöf property and σ-fragmentability." Fundamenta Mathematicae 180.2 (2003): 161-183. <http://eudml.org/doc/282583>.

@article{B2003,
abstract = {In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space $[-1,1]^\{D\}$ is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of $[-1,1]^\{D\}$ is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is the case then $(X,γ(D))^\{ℕ\}$ is also Lindelöf. We give several applications of this theorem in areas of topology and Banach spaces. We also show by examples that the main theorem cannot be extended to the cases where X is Čech-analytic and Lindelöf or countably K-determined.},
author = {B. Cascales, I. Namioka},
journal = {Fundamenta Mathematicae},
keywords = {-analytic spaces; Lindelöf spaces; -fragmentability; -topology; Corson compact spaces; compact perfect sets},
language = {eng},
number = {2},
pages = {161-183},
title = {The Lindelöf property and σ-fragmentability},
url = {http://eudml.org/doc/282583},
volume = {180},
year = {2003},
}

TY - JOUR
AU - B. Cascales
AU - I. Namioka
TI - The Lindelöf property and σ-fragmentability
JO - Fundamenta Mathematicae
PY - 2003
VL - 180
IS - 2
SP - 161
EP - 183
AB - In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space $[-1,1]^{D}$ is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of $[-1,1]^{D}$ is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is the case then $(X,γ(D))^{ℕ}$ is also Lindelöf. We give several applications of this theorem in areas of topology and Banach spaces. We also show by examples that the main theorem cannot be extended to the cases where X is Čech-analytic and Lindelöf or countably K-determined.
LA - eng
KW - -analytic spaces; Lindelöf spaces; -fragmentability; -topology; Corson compact spaces; compact perfect sets
UR - http://eudml.org/doc/282583
ER -