Combinatorics of open covers (VIII)

Liljana Babinkostova; Ljubiša D.R. Kočinac; Marion Scheepers

doi:10.1016/j.topol.2003.08.019

Combinatorics of open covers (VIII)

Liljana Babinkostova
, Ljubiša D.R. Kočinac
, Marion Scheepers

Mathematics Department

University of Nis

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

For each space, U_fin(Γ,Ω) is equivalent to S_fin(Ω,O^wgp) and this selection property has game-theoretic and Ramsey-theoretic characterizations (Theorem 2). For Lindelöf space X we characterize when a subspace Y is relatively Hurewicz in X in terms of selection principles (Theorem 9), and for metrizable X in terms of basis properties, and measurelike properties (Theorems 14 and 16). Using the Continuum Hypothesis we show that there is a subset Y of the Cantor set C which has the relative γ-property in C, but Y does not have the Menger property.

Original language	English
Pages (from-to)	15-32
Number of pages	18
Journal	Topology and its Applications
Volume	140
Issue number	1 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.topol.2003.08.019
State	Published - 14 May 2004

Keywords

Game theory
Groupable cover
Hurewicz basis property
Hurewicz measure zero
Hurewicz property
Ramsey theory
Relative Hurewicz property
Relative γ-set
S(Ω,Λ)
U(Γ,Ω)
Weakly groupable cover

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10.1016/j.topol.2003.08.019

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title = "Combinatorics of open covers (VIII)",

abstract = "For each space, Ufin(Γ,Ω) is equivalent to Sfin(Ω,Owgp) and this selection property has game-theoretic and Ramsey-theoretic characterizations (Theorem 2). For Lindel{\"o}f space X we characterize when a subspace Y is relatively Hurewicz in X in terms of selection principles (Theorem 9), and for metrizable X in terms of basis properties, and measurelike properties (Theorems 14 and 16). Using the Continuum Hypothesis we show that there is a subset Y of the Cantor set C which has the relative γ-property in C, but Y does not have the Menger property.",

keywords = "Game theory, Groupable cover, Hurewicz basis property, Hurewicz measure zero, Hurewicz property, Ramsey theory, Relative Hurewicz property, Relative γ-set, S(Ω,Λ), U(Γ,Ω), Weakly groupable cover",

author = "Liljana Babinkostova and Ko{\v c}inac, \{Ljubi{\v s}a D.R.\} and Marion Scheepers",

year = "2004",

month = may,

day = "14",

doi = "10.1016/j.topol.2003.08.019",

language = "English",

volume = "140",

pages = "15--32",

number = "1 SPEC. ISS.",

}

TY - JOUR

T1 - Combinatorics of open covers (VIII)

AU - Babinkostova, Liljana

AU - Kočinac, Ljubiša D.R.

AU - Scheepers, Marion

PY - 2004/5/14

Y1 - 2004/5/14

N2 - For each space, Ufin(Γ,Ω) is equivalent to Sfin(Ω,Owgp) and this selection property has game-theoretic and Ramsey-theoretic characterizations (Theorem 2). For Lindelöf space X we characterize when a subspace Y is relatively Hurewicz in X in terms of selection principles (Theorem 9), and for metrizable X in terms of basis properties, and measurelike properties (Theorems 14 and 16). Using the Continuum Hypothesis we show that there is a subset Y of the Cantor set C which has the relative γ-property in C, but Y does not have the Menger property.

AB - For each space, Ufin(Γ,Ω) is equivalent to Sfin(Ω,Owgp) and this selection property has game-theoretic and Ramsey-theoretic characterizations (Theorem 2). For Lindelöf space X we characterize when a subspace Y is relatively Hurewicz in X in terms of selection principles (Theorem 9), and for metrizable X in terms of basis properties, and measurelike properties (Theorems 14 and 16). Using the Continuum Hypothesis we show that there is a subset Y of the Cantor set C which has the relative γ-property in C, but Y does not have the Menger property.

KW - Game theory

KW - Groupable cover

KW - Hurewicz basis property

KW - Hurewicz measure zero

KW - Hurewicz property

KW - Ramsey theory

KW - Relative Hurewicz property

KW - Relative γ-set

KW - S(Ω,Λ)

KW - U(Γ,Ω)

KW - Weakly groupable cover

UR - https://www.scopus.com/pages/publications/1942508914

U2 - 10.1016/j.topol.2003.08.019

DO - 10.1016/j.topol.2003.08.019

M3 - Article

AN - SCOPUS:1942508914

SN - 0166-8641

VL - 140

SP - 15

EP - 32

JO - Topology and its Applications

JF - Topology and its Applications

IS - 1 SPEC. ISS.

ER -

Combinatorics of open covers (VIII)

Abstract

Keywords

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