“Banach game”的意思、由来-开放百科全书

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Banach game

释义

References
Further reading

In mathematics, the Banach game is a topological game introduced by Stefan Banach in 1935 in the second addendum to problem 43 of the Scottish book as a variation of the Banach–Mazur game.^[1]

Given a subset of real numbers, two players alternatively write down arbitrary (not necessarily in ) positive real numbers such that Player one wins if and only if exists and is in .^[2]

One observation about the game is that if is a countable set, then either of the players can cause the final sum to avoid the set.{{sfn|Mauldin|1981|p=116}} Thus in this situation the second player can win.

References

1. ^{{cite book|last1=Mauldin|first1=R. Daniel|title=The Scottish Book: Mathematics from the Scottish Cafe|date=April 1981|publisher=Birkhäuser|isbn=978-3-7643-3045-3|page=113|edition=1|url=http://users.auth.gr/siskakis/The%20Scottish%20book.pdf}}
2. ^{{cite journal|last1=Telgársky|first1=Rastislav|title=Topological Games: On the 50th Anniversary of the Banach–Mazur Game|journal=Rocky Mountain Journal of Mathematics|date=Spring 1987|volume=17|issue=2|pages=227–276|url=http://www.telgarsky.com/1987-RMJM-Telgarsky-Topological-Games.pdf}} at 242.

References

Further reading