On the strategies for NONEMPTY in topological games


ÖNAL S. , Soyarslan S.

TOPOLOGY AND ITS APPLICATIONS, cilt.278, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 278
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1016/j.topol.2020.107236
  • Dergi Adı: TOPOLOGY AND ITS APPLICATIONS

Özet

We prove that if NONEMPTY has a Markov strategy in the Choquet game on a space X, then the player has a 2-tactic in that game. We also prove that if NONEMPTY has a k-Markov strategy in the Choquet game on a space X which has a Noetherian base with countable rank, then the player has a k-tactic in that game. We show that if NONEMPTY has a winning strategy in the Choquet game on a space X which has one of the some special bases including sigma-locally countable bases, then the player has a 2-tactic in that game. We also show that if NONEMPTY has a winning strategy in the Choquet game on a space X which has some special Noetherian bases, then NONEMPTY has a stationary strategy, 1-tactic, in that game. We investigate some similar results for the Banach-Mazur game. (C) 2020 Elsevier B.V. All rights reserved.