On the strategies for NONEMPTY in topological games


ÖNAL S., Soyarslan S.

TOPOLOGY AND ITS APPLICATIONS, vol.278, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 278
  • Publication Date: 2020
  • Doi Number: 10.1016/j.topol.2020.107236
  • Journal Name: TOPOLOGY AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Gazi University Affiliated: Yes

Abstract

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.