Abstract
This chapter illustrates some of the trends in the study of topological games. It studies the question as to whether some well-known topological property is characterized by the existence/non-existence of a winning strategy of some player of the game; the game is usually a powerful tool in analyzing the corresponding topological property. Many well-known topological concepts that were introduced and studied long before the games were invented are now characterized by games; in games sometimes neither player has a winning strategy. A perfect information strategy is a function that has the sequence of all prior moves of the opponent as input, and has the response of the strategy owner as output. There are now numerous examples of topological games. This chapter briefly describes two particularly important classes of games: nested chain games and diagonalization games. The classical Banach–Mazur game from the Scottish Book is probably the best known example of an infinite topological nested chain game. The class of diagonalization games is at least as important as the nested chain games and also has a long history.
Original language | English |
---|---|
Title of host publication | Encyclopedia of General Topology |
Pages | 439-442 |
Number of pages | 4 |
ISBN (Electronic) | 9780444503558 |
DOIs | |
State | Published - 1 Jan 2003 |