Rothberger Bounded Groups and Ramsey Theory

Marion Scheepers

doi:10.1016/j.topol.2011.05.025

Rothberger Bounded Groups and Ramsey Theory

Marion Scheepers

Mathematics Department

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

9 Scopus citations

Abstract

We show that:

(1) Rothberger bounded subgroups of σ-compact groups are characterized by Ramseyan partition relations (Corollary 4).

(2) For each uncountable cardinal κ there is a T₀ topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is not a closed subspace of any σ-compact space (Theorem 8).

(3) For each uncountable cardinal κ there is a T₀ topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is σ-compact (Corollary 17).

Original language	American English
Pages (from-to)	1575-1583
Number of pages	9
Journal	Topology and its Applications
Volume	158
Issue number	13
DOIs	https://doi.org/10.1016/j.topol.2011.05.025
State	Published - 15 Aug 2011

Keywords

Infinite game
Ramsey theory
Rothberger bounded
Strong measure zero
Topological group
Uniformizable space

EGS Disciplines

Mathematics

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10.1016/j.topol.2011.05.025

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title = "Rothberger Bounded Groups and Ramsey Theory",

abstract = "We show that: (1) Rothberger bounded subgroups of σ-compact groups are characterized by Ramseyan partition relations (Corollary 4). (2) For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is not a closed subspace of any σ-compact space (Theorem 8). (3) For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is σ-compact (Corollary 17).",

keywords = "Infinite game, Ramsey theory, Rothberger bounded, Strong measure zero, Topological group, Uniformizable space",

author = "Marion Scheepers",

year = "2011",

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doi = "10.1016/j.topol.2011.05.025",

language = "American English",

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T1 - Rothberger Bounded Groups and Ramsey Theory

AU - Scheepers, Marion

PY - 2011/8/15

Y1 - 2011/8/15

N2 - We show that: (1) Rothberger bounded subgroups of σ-compact groups are characterized by Ramseyan partition relations (Corollary 4). (2) For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is not a closed subspace of any σ-compact space (Theorem 8). (3) For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is σ-compact (Corollary 17).

AB - We show that: (1) Rothberger bounded subgroups of σ-compact groups are characterized by Ramseyan partition relations (Corollary 4). (2) For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is not a closed subspace of any σ-compact space (Theorem 8). (3) For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is σ-compact (Corollary 17).

KW - Infinite game

KW - Ramsey theory

KW - Rothberger bounded

KW - Strong measure zero

KW - Topological group

KW - Uniformizable space

UR - http://www.scopus.com/inward/record.url?scp=79959975897&partnerID=8YFLogxK

UR - https://scholarworks.boisestate.edu/math_facpubs/67

U2 - 10.1016/j.topol.2011.05.025

DO - 10.1016/j.topol.2011.05.025

M3 - Article

SN - 0016-660X

VL - 158

SP - 1575

EP - 1583

JO - Topology and its Applications

JF - Topology and its Applications

IS - 13

ER -

Rothberger Bounded Groups and Ramsey Theory

Abstract

Keywords

EGS Disciplines

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