Spaces related to gamma-sets
Stationary and convergent strategies in Choquet games
If Nonempty has a winning strategy against Empty in the Choquet game on a space, the space is said to be a Choquet space. Such a winning strategy allows Nonempty to consider the entire finite history of previous moves before making each new move; a stationary strategy only permits Nonempty to consider the previous move by Empty. We show that Nonempty has a stationary winning strategy for every second-countable T₁ Choquet space. More generally, Nonempty has a stationary winning strategy for...
The even-odd hat problem
We answer a question of C. Hardin and A. Taylor concerning a hat-guessing game.
The game of Cutblock.
Undetermined sets of point-open games
We show that a set of reals is undetermined in Galvin's point-open game iff it is uncountable and has property C", which answers a question of Gruenhage.
Weakly α-favourable measure spaces
I discuss the properties of α-favourable and weakly α-favourable measure spaces, with remarks on their relations with other classes.
Winning positions in simplicial Nim.