A semifilter approach to selection principles II: τ * -covers

Lubomyr Zdomsky

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 3, page 539-547
  • ISSN: 0010-2628

Abstract

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Developing the idea of assigning to a large cover of a topological space a corresponding semifilter, we show that every Menger topological space has the property ⋃ fin ( 𝒪 , T * ) provided ( 𝔲 < 𝔤 ) , and every space with the property ⋃ fin ( 𝒪 , T * ) is Hurewicz provided ( Depth + ( [ ω ] ℵ 0 ) ≤ 𝔟 ) . Combining this with the results proven in cited literature, we settle all questions whether (it is consistent that) the properties P and Q [do not] coincide, where P and Q run over ⋃ fin ( 𝒪 , Γ ) , ⋃ fin ( 𝒪 , T ) , ⋃ fin ( 𝒪 , T * ) , ⋃ fin ( 𝒪 , Ω ) , and ⋃ fin ( 𝒪 , 𝒪 ) .

How to cite

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Zdomsky, Lubomyr. "A semifilter approach to selection principles II: $\tau ^\ast $-covers." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 539-547. <http://eudml.org/doc/249868>.

@article{Zdomsky2006,
abstract = {Developing the idea of assigning to a large cover of a topological space a corresponding semifilter, we show that every Menger topological space has the property $\bigcup _\{\operatorname\{fin\}\}(\mathcal \{O\}, \operatorname\{T\}^\ast )$ provided $(\mathfrak \{u\}<\mathfrak \{g\})$, and every space with the property $\bigcup _\{\operatorname\{fin\}\}(\mathcal \{O\}, \operatorname\{T\}^\ast )$ is Hurewicz provided $(\operatorname\{Depth\}^+([\omega ]^\{\aleph _0\})\le \mathfrak \{b\})$. Combining this with the results proven in cited literature, we settle all questions whether (it is consistent that) the properties $\text\{P\}$ and $\text\{Q\}$ [do not] coincide, where $\text\{P\}$ and $\text\{Q\}$ run over $\bigcup _\{\operatorname\{fin\}\}(\mathcal \{O\},\Gamma )$, $\bigcup _\{\operatorname\{fin\}\}(\mathcal \{O\}, \operatorname\{T\})$, $\bigcup _\{\operatorname\{fin\}\}(\mathcal \{O\}, \operatorname\{T\}^\ast )$, $\bigcup _\{\operatorname\{fin\}\}(\mathcal \{O\}, \Omega )$, and $\bigcup _\{\operatorname\{fin\}\}(\mathcal \{O\}, \mathcal \{O\})$.},
author = {Zdomsky, Lubomyr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {selection principle; semifilter; small cardinals; selection principle; semifilter; small cardinals},
language = {eng},
number = {3},
pages = {539-547},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A semifilter approach to selection principles II: $\tau ^\ast $-covers},
url = {http://eudml.org/doc/249868},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Zdomsky, Lubomyr
TI - A semifilter approach to selection principles II: $\tau ^\ast $-covers
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 3
SP - 539
EP - 547
AB - Developing the idea of assigning to a large cover of a topological space a corresponding semifilter, we show that every Menger topological space has the property $\bigcup _{\operatorname{fin}}(\mathcal {O}, \operatorname{T}^\ast )$ provided $(\mathfrak {u}<\mathfrak {g})$, and every space with the property $\bigcup _{\operatorname{fin}}(\mathcal {O}, \operatorname{T}^\ast )$ is Hurewicz provided $(\operatorname{Depth}^+([\omega ]^{\aleph _0})\le \mathfrak {b})$. Combining this with the results proven in cited literature, we settle all questions whether (it is consistent that) the properties $\text{P}$ and $\text{Q}$ [do not] coincide, where $\text{P}$ and $\text{Q}$ run over $\bigcup _{\operatorname{fin}}(\mathcal {O},\Gamma )$, $\bigcup _{\operatorname{fin}}(\mathcal {O}, \operatorname{T})$, $\bigcup _{\operatorname{fin}}(\mathcal {O}, \operatorname{T}^\ast )$, $\bigcup _{\operatorname{fin}}(\mathcal {O}, \Omega )$, and $\bigcup _{\operatorname{fin}}(\mathcal {O}, \mathcal {O})$.
LA - eng
KW - selection principle; semifilter; small cardinals; selection principle; semifilter; small cardinals
UR - http://eudml.org/doc/249868
ER -

References

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