TY - JOUR
T1 - Ramsey theory and the borel conjecture
AU - Scheepers, Marion
N1 - Publisher Copyright:
© 2020 American Mathematical Society.
PY - 2020
Y1 - 2020
N2 - The Borel covering property, introduced a century ago by E. Borel, is intimately connected with Ramsey theory, initiated ninety years ago in an influential paper of F.P. Ramsey. The current state of knowledge about the connection between the Borel covering property and Ramsey theory is outlined in this paper. Initially the connection is established for the situation when the set with the Borel covering property is a proper subset of a σ-compact uniform space. Then the connection is explored for a stronger covering property introduced by Rothberger. After establishing the fact that in this case several landmark Ramseyan theorems are characteristic of this stronger covering property, the case when the space with this stronger covering property is in fact σ-compact is explored.
AB - The Borel covering property, introduced a century ago by E. Borel, is intimately connected with Ramsey theory, initiated ninety years ago in an influential paper of F.P. Ramsey. The current state of knowledge about the connection between the Borel covering property and Ramsey theory is outlined in this paper. Initially the connection is established for the situation when the set with the Borel covering property is a proper subset of a σ-compact uniform space. Then the connection is explored for a stronger covering property introduced by Rothberger. After establishing the fact that in this case several landmark Ramseyan theorems are characteristic of this stronger covering property, the case when the space with this stronger covering property is in fact σ-compact is explored.
KW - Infinite game
KW - Ramsey theory
KW - Rothberger bounded
KW - Strong measure zero
KW - Topological group
KW - Uni-formizable space
UR - http://www.scopus.com/inward/record.url?scp=85091360894&partnerID=8YFLogxK
U2 - 10.1090/conm/755/15177
DO - 10.1090/conm/755/15177
M3 - Article
AN - SCOPUS:85091360894
SN - 0271-4132
VL - 755
SP - 69
EP - 113
JO - Contemporary Mathematics
JF - Contemporary Mathematics
ER -