TY - JOUR
T1 - An infinite game on groups
AU - Babinkostova, Liljana
AU - Scheepers, Marion
PY - 2004
Y1 - 2004
N2 - We consider an infinite game on a group G, defined relative to a subset A of G. The game is denoted G(G,A). The finite version of the game, introduced in [1], was inspired by an attack on the RSA cryptosystem as used in an implementation of SSL. Besides identifying circumstances under which player TWO does not have a winning strategy, we show for the topological group of real numbers that if C is a set of real numbers having a selection property (*) introduced by Gerlits and Nagy, then for any interval J of positive length, TWO has a winning strategy in the game G(ℝ J ∪ C).
AB - We consider an infinite game on a group G, defined relative to a subset A of G. The game is denoted G(G,A). The finite version of the game, introduced in [1], was inspired by an attack on the RSA cryptosystem as used in an implementation of SSL. Besides identifying circumstances under which player TWO does not have a winning strategy, we show for the topological group of real numbers that if C is a set of real numbers having a selection property (*) introduced by Gerlits and Nagy, then for any interval J of positive length, TWO has a winning strategy in the game G(ℝ J ∪ C).
KW - Game
KW - Group
KW - Selection principle
KW - Winning strategy
UR - https://www.scopus.com/pages/publications/85032379312
U2 - 10.14321/realanalexch.29.2.0739
DO - 10.14321/realanalexch.29.2.0739
M3 - Article
AN - SCOPUS:85032379312
SN - 0147-1937
VL - 29
SP - 739
EP - 754
JO - Real Analysis Exchange
JF - Real Analysis Exchange
IS - 2
ER -