Centenary of the Borel Conjecture

In 1919 Emile Borel noted that countable sets of real numbers have a certain covering property, and speculated that only countable sets of real numbers have that property. Here, mathematicians explore the history and impact of the Borel conjecture during the intervening century. They cover game-theory aspects of the Borel conjecture; strong measure zero in Polish groups; Ramsey theory and the Borel conjecture; the algebraic union of strongly measure zero sets and their relatives with sets of real numbers; Borel conjecture, dual Borel conjectures, and other variants of the Borel conjecture; and selection principles in the Laver, Miller, and Sacks models. Annotation ©2020 Ringgold, Inc., Portland, OR (protoview.com)