Stationary and convergent strategies in Choquet games

François G. Dorais, and Carl Mummert. "Stationary and convergent strategies in Choquet games." Fundamenta Mathematicae 209.1 (2010): 59-79. <http://eudml.org/doc/286389>.

@article{FrançoisG2010,
abstract = { 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 any T₁ Choquet space with an open-finite basis. We also study convergent strategies for the Choquet game, proving the following results. A T₁ space X is the open continuous image of a complete metric space if and only if Nonempty has a convergent winning strategy in the Choquet game on X. A T₁ space X is the open continuous compact image of a metric space if and only if X is metacompact and Nonempty has a stationary convergent strategy in the Choquet game on X. A T₁ space X is the open continuous compact image of a complete metric space if and only if X is metacompact and Nonempty has a stationary convergent winning strategy in the Choquet game on X. },
author = {François G. Dorais, Carl Mummert},
journal = {Fundamenta Mathematicae},
keywords = {Choquet game; stationary strategy; convergent strategy; open-finite base},
language = {eng},
number = {1},
pages = {59-79},
title = {Stationary and convergent strategies in Choquet games},
url = {http://eudml.org/doc/286389},
volume = {209},
year = {2010},
}

TY - JOUR
AU - François G. Dorais
AU - Carl Mummert
TI - Stationary and convergent strategies in Choquet games
JO - Fundamenta Mathematicae
PY - 2010
VL - 209
IS - 1
SP - 59
EP - 79
AB - 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 any T₁ Choquet space with an open-finite basis. We also study convergent strategies for the Choquet game, proving the following results. A T₁ space X is the open continuous image of a complete metric space if and only if Nonempty has a convergent winning strategy in the Choquet game on X. A T₁ space X is the open continuous compact image of a metric space if and only if X is metacompact and Nonempty has a stationary convergent strategy in the Choquet game on X. A T₁ space X is the open continuous compact image of a complete metric space if and only if X is metacompact and Nonempty has a stationary convergent winning strategy in the Choquet game on X.
LA - eng
KW - Choquet game; stationary strategy; convergent strategy; open-finite base
UR - http://eudml.org/doc/286389
ER -