The Hurewicz covering property and slaloms in the Baire space

Boaz Tsaban. "The Hurewicz covering property and slaloms in the Baire space." Fundamenta Mathematicae 181.3 (2004): 273-280. <http://eudml.org/doc/282879>.

@article{BoazTsaban2004,
abstract = {According to a result of Kočinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals X has the Hurewicz property if, and only if, each large open cover of X contains a groupable subcover. This solves in the affirmative a problem of Scheepers. The proof uses a rigorously justified abuse of notation and a "structure" counterpart of a combinatorial characterization, in terms of slaloms, of the minimal cardinality 𝔟 of an unbounded family of functions in the Baire space. In particular, we obtain a new characterization of 𝔟.},
author = {Boaz Tsaban},
journal = {Fundamenta Mathematicae},
keywords = {Hurewicz property; Menger property; large covers; groupability; slalom; unbounding number },
language = {eng},
number = {3},
pages = {273-280},
title = {The Hurewicz covering property and slaloms in the Baire space},
url = {http://eudml.org/doc/282879},
volume = {181},
year = {2004},
}

TY - JOUR
AU - Boaz Tsaban
TI - The Hurewicz covering property and slaloms in the Baire space
JO - Fundamenta Mathematicae
PY - 2004
VL - 181
IS - 3
SP - 273
EP - 280
AB - According to a result of Kočinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals X has the Hurewicz property if, and only if, each large open cover of X contains a groupable subcover. This solves in the affirmative a problem of Scheepers. The proof uses a rigorously justified abuse of notation and a "structure" counterpart of a combinatorial characterization, in terms of slaloms, of the minimal cardinality 𝔟 of an unbounded family of functions in the Baire space. In particular, we obtain a new characterization of 𝔟.
LA - eng
KW - Hurewicz property; Menger property; large covers; groupability; slalom; unbounding number 
UR - http://eudml.org/doc/282879
ER -