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https://doi.org/10.3336/gm.43.1.14

One more variation of the point-open game

Arcos Daniel Jardón ; Departamento de Matemáticas, Universidad Autónoma Metropolitana
Vladimir V. Tkachuk ; Departamento de Matemáticas, Universidad Autónoma Metropolitana

Puni tekst: engleski, pdf (164 KB) str. 205-217 preuzimanja: 318* citiraj
APA 6th Edition
Jardón, A.D. i Tkachuk, V.V. (2008). One more variation of the point-open game. Glasnik matematički, 43 (1), 205-217. https://doi.org/10.3336/gm.43.1.14
MLA 8th Edition
Jardón, Arcos Daniel i Vladimir V. Tkachuk. "One more variation of the point-open game." Glasnik matematički, vol. 43, br. 1, 2008, str. 205-217. https://doi.org/10.3336/gm.43.1.14. Citirano 28.09.2021.
Chicago 17th Edition
Jardón, Arcos Daniel i Vladimir V. Tkachuk. "One more variation of the point-open game." Glasnik matematički 43, br. 1 (2008): 205-217. https://doi.org/10.3336/gm.43.1.14
Harvard
Jardón, A.D., i Tkachuk, V.V. (2008). 'One more variation of the point-open game', Glasnik matematički, 43(1), str. 205-217. https://doi.org/10.3336/gm.43.1.14
Vancouver
Jardón AD, Tkachuk VV. One more variation of the point-open game. Glasnik matematički [Internet]. 2008 [pristupljeno 28.09.2021.];43(1):205-217. https://doi.org/10.3336/gm.43.1.14
IEEE
A.D. Jardón i V.V. Tkachuk, "One more variation of the point-open game", Glasnik matematički, vol.43, br. 1, str. 205-217, 2008. [Online]. https://doi.org/10.3336/gm.43.1.14

Sažetak
A topological game "Dense Gδσ-sets" (also denoted by DG) is introduced as follows: for any n ω at the n-th move the player I takes a point xn v X and II responds by taking a Gδ-set Qn in the space X such that xn Qn. The play stops after ω moves and I wins if the set {Qn : n ω} is dense in X. Otherwise the player II is declared to be the winner. We study classes of spaces on which the player I has a winning strategy. It is evident that the I-favorable spaces constitute a generalization of the class of separable spaces. We show that there exists a neutral space for the game DG and prove, among other things, that Lindelöf scattered spaces and dyadic spaces are I-favorable. We characterize I-favorability for the game DG in the spaces Cp(X); one of the applications is that, for a Lindelöf Σ-space X, the space Cp(X) is I-favorable for DG if and only if X is ω-monolithic.

Ključne riječi
Topological game; player; winning strategy; dense Gδσ-sets; separable space; dyadic compact space; scattered compact space; neutral space; function space

Hrčak ID: 23541

URI
https://hrcak.srce.hr/23541

Posjeta: 552 *