| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Catania, Dept Math, Viale A Doria 6, I-95125 Catania - Italy
[3] Univ Fed ABC, Ctr Matemat Comp & Cognicao, Ave Estados 5001, BR-09210580 Santo Andre, SP - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Israel Journal of Mathematics; v. 224, n. 1, p. 133-158, APR 2018. |
| Web of Science Citations: | 3 |
| Abstract | |
For a topological space X and a point x is an element of X, consider the following game-related to the property of X being countably tight at x. In each inning n is an element of omega, the first player chooses a set A(n) that clusters at x, and then the second player picks a point a (n) is an element of A(n) ; the second player is the winner if and only if x is an element of([a(n) : n is an element of omega]) over bar. In this work, we study variations of this game in which the second player is allowed to choose finitely many points per inning rather than one, but in which the number of points they are allowed to choose in each inning has been fixed in advance. Surprisingly, if the number of points allowed per inning is the same throughout the play, then all of the games obtained in this fashion are distinct. We also show that a new game is obtained if the number of points the second player is allowed to pick increases at each inning. (AU) | |
| FAPESP's process: | 13/05469-7 - Topological games, selection principles and covering properties |
| Grantee: | Leandro Fiorini Aurichi |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 12/09214-0 - Topological games and applications in General Topology |
| Grantee: | Rodrigo Roque Dias |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |