# The Banach--Mazur game and the strong Choquet game in domain theory

Source: [The Banach--Mazur game and the strong Choquet game in domain theory](<https://www.sota2.com/research/paper/68fa54ea1e209131ce98fac7>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T13:16:35.702Z

Authors: Judyta B\\k{a}k, Andrzej Kucharski

Published: 2018-06-03T12:57:15.000Z

## Abstract

We prove that a player $\\alpha$ has a winning strategy in the Banach--Mazur game on a space $X$ if and only if $X$ is F-Y countably $\\pi$-domain representable. We show that Choquet complete spaces are F-Y countably domain representable. We give an example of a space, which is F-Y countably domain representable, but it is not F-Y $\\pi$-domain representable.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1806.00785>)

[PDF](<https://arxiv.org/pdf/1806.00785.pdf>)