Combinatorics of open covers (VII): Groupability

Ljubiša D. R. Kočinac, and Marion Scheepers. "Combinatorics of open covers (VII): Groupability." Fundamenta Mathematicae 179.2 (2003): 131-155. <http://eudml.org/doc/282608>.

@article{LjubišaD2003,
abstract = {We use Ramseyan partition relations to characterize: ∙ the classical covering property of Hurewicz; ∙ the covering property of Gerlits and Nagy; ∙ the combinatorial cardinal numbers and add(ℳ ). Let X be a $T_\{31/2\}$-space. In [9] we showed that $C_\{p\}(X)$ has countable strong fan tightness as well as the Reznichenko property if, and only if, all finite powers of X have the Gerlits-Nagy covering property. Now we show that the following are equivalent: 1. $C_\{p\}(X)$ has countable fan tightness and the Reznichenko property. 2. All finite powers of X have the Hurewicz property. We show that for $C_\{p\}(X)$ the combination of countable fan tightness with the Reznichenko property is characterized by a Ramseyan partition relation. Extending the work in [9], we give an analogous Ramseyan characterization for the combination of countable strong fan tightness with the Reznichenko property on $C_\{p\}(X)$.},
author = {Ljubiša D. R. Kočinac, Marion Scheepers},
journal = {Fundamenta Mathematicae},
keywords = {Hurewicz property; Reznichenko property; Gerlits-Nagy property; countable fan tightness; Ramsey theory; game theory},
language = {eng},
number = {2},
pages = {131-155},
title = {Combinatorics of open covers (VII): Groupability},
url = {http://eudml.org/doc/282608},
volume = {179},
year = {2003},
}

TY - JOUR
AU - Ljubiša D. R. Kočinac
AU - Marion Scheepers
TI - Combinatorics of open covers (VII): Groupability
JO - Fundamenta Mathematicae
PY - 2003
VL - 179
IS - 2
SP - 131
EP - 155
AB - We use Ramseyan partition relations to characterize: ∙ the classical covering property of Hurewicz; ∙ the covering property of Gerlits and Nagy; ∙ the combinatorial cardinal numbers and add(ℳ ). Let X be a $T_{31/2}$-space. In [9] we showed that $C_{p}(X)$ has countable strong fan tightness as well as the Reznichenko property if, and only if, all finite powers of X have the Gerlits-Nagy covering property. Now we show that the following are equivalent: 1. $C_{p}(X)$ has countable fan tightness and the Reznichenko property. 2. All finite powers of X have the Hurewicz property. We show that for $C_{p}(X)$ the combination of countable fan tightness with the Reznichenko property is characterized by a Ramseyan partition relation. Extending the work in [9], we give an analogous Ramseyan characterization for the combination of countable strong fan tightness with the Reznichenko property on $C_{p}(X)$.
LA - eng
KW - Hurewicz property; Reznichenko property; Gerlits-Nagy property; countable fan tightness; Ramsey theory; game theory
UR - http://eudml.org/doc/282608
ER -