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Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Topological_game> ?p ?o }

• Topological_game abstract "A topological game is an infinite game of perfect information played between two players on a topological space. Players choose objects with topological properties such as points, open sets, closed sets and open coverings. Time is generally discrete, but the plays may have transfinite lengths, and extensions to continuum time have been put forth. The conditions for a player to win can involve notions like topological closure and convergence.It turns out that some fundamental topological constructions have a natural counterpart in topological games; examples of these are the Baire property, Baire spaces, completeness and convergence properties, separation properties, covering and base properties, continuous images, Suslin sets, and singular spaces. At the same time, some topological properties that arise naturally in topological games can be generalized beyond a game-theoretic context: by virtue of this duality, topological games have been widely used to describe new properties of topological spaces, and to put known properties under a different light.The term topological game was first introduced by Berge, who defined the basic ideas and formalism in analogy with topological groups. A different meaning for topological game, the concept of “topological properties defined by games”, was introduced in the paper of Rastislav Telgársky, and later \"spaces defined by topological games\"; this approach is based on analogies with matrix games, differential games and statistical games, and defines and studies topological games within topology. After more than 35 years, the term “topological game” became widespread, and appeared in several hundreds of publications. The survey paper of Telgársky emphasizes the origin of topological games from the Banach–Mazur game.There are two other meanings of topological games, but these are used less frequently. The term topological game introduced by Leon Petrosjan in the study of antagonistic pursuit-evasion games. The trajectories in these topological games are continuous in time. The games of Nash (the Hex games), the Milnor games (Y games), the Shapley games (projective plane games), and Gale's games (Bridg-It games) were called topological games by David Gale in his invited address [1979/80]. The number of moves in these games is always finite. The discovery or rediscovery of these topological games goes back to years 1948–49.↑ ↑ ↑ ↑ ↑ ↑ ↑".
• Topological_game wikiPageID "15334997".
• Topological_game wikiPageLength "9021".
• Topological_game wikiPageOutDegree "31".
• Topological_game wikiPageRevisionID "702370070".
• Topological_game wikiPageWikiLink Axiom_of_choice.
• Topological_game wikiPageWikiLink Baire_space.
• Topological_game wikiPageWikiLink Banach_game.
• Topological_game wikiPageWikiLink Banach–Mazur_game.
• Topological_game wikiPageWikiLink Binary_game.
• Topological_game wikiPageWikiLink Category:General_topology.
• Topological_game wikiPageWikiLink Category:Topological_games.
• Topological_game wikiPageWikiLink Choquet_game.
• Topological_game wikiPageWikiLink Closed_graph_theorem.
• Topological_game wikiPageWikiLink Closure_(topology).
• Topological_game wikiPageWikiLink Differential_game.
• Topological_game wikiPageWikiLink Hex_(board_game).
• Topological_game wikiPageWikiLink Kazimierz_Kuratowski.
• Topological_game wikiPageWikiLink Luzin.
• Topological_game wikiPageWikiLink Meagre_set.
• Topological_game wikiPageWikiLink Ordinal_number.
• Topological_game wikiPageWikiLink Partially_ordered_set.
• Topological_game wikiPageWikiLink Perfect_information.
• Topological_game wikiPageWikiLink Property_of_Baire.
• Topological_game wikiPageWikiLink Pursuit-evasion.
• Topological_game wikiPageWikiLink Stanislaw_Ulam.
• Topological_game wikiPageWikiLink Topological_space.
• Topological_game wikiPageWikiLink Transfinite_number.
• Topological_game wikiPageWikiLink Ultrafilter.
• Topological_game wikiPageWikiLink Wikt:convergence.
• Topological_game wikiPageWikiLinkText "Markov winning strategy".
• Topological_game wikiPageWikiLinkText "Sierpiński game".
• Topological_game wikiPageWikiLinkText "Topological game".
• Topological_game wikiPageWikiLinkText "stationary winning strategy".
• Topological_game wikiPageWikiLinkText "strong Choquet game".
• Topological_game wikiPageWikiLinkText "topological game".
• Topological_game wikiPageUsesTemplate Template:Main.
• Topological_game wikiPageUsesTemplate Template:Reflist.
• Topological_game subject Category:General_topology.
• Topological_game subject Category:Topological_games.
• Topological_game hypernym Game.
• Topological_game type VideoGame.
• Topological_game type Concept.
• Topological_game comment "A topological game is an infinite game of perfect information played between two players on a topological space. Players choose objects with topological properties such as points, open sets, closed sets and open coverings. Time is generally discrete, but the plays may have transfinite lengths, and extensions to continuum time have been put forth.".
• Topological_game label "Topological game".
• Topological_game sameAs Q7825035.
• Topological_game sameAs m.03m5cfx.
• Topological_game sameAs Q7825035.
• Topological_game wasDerivedFrom Topological_game?oldid=702370070.
• Topological_game isPrimaryTopicOf Topological_game.