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299:, then either of the players can cause the final sum to avoid the set. Thus in this situation the second player has a
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390:"Existence of nondetermined sets for some two person games over reals"
347:"Topological Games: On the 50th Anniversary of the Banach–Mazur Game"
66:, two players alternatively write down arbitrary (not necessarily in
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The
Scottish Book: Mathematics from the Scottish Cafe
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31:
in 1935 in the second addendum to problem 43 of the
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197:{\displaystyle x_{0}>x_{1}>x_{2}>\cdots }
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275:One observation about the game is that if
245:{\displaystyle \sum _{i=0}^{\infty }x_{i}}
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138:{\displaystyle x_{0},x_{1},x_{2},\ldots }
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324:(1 ed.). Birkhäuser. p. 113.
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354:Rocky Mountain Journal of Mathematics
7:
345:Telgársky, Rastislav (Spring 1987).
227:
14:
320:Mauldin, R. Daniel (April 1981).
204:Player one wins if and only if
388:Moran, Gadi (September 1971).
1:
395:Israel Journal of Mathematics
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86:) positive real numbers
16:Topological game in math
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35:as a variation of the
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19:In mathematics, the
409:10.1007/BF02771682
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427:Topological games
331:978-3-7643-3045-3
288:{\displaystyle X}
265:{\displaystyle X}
252:exists and is in
79:{\displaystyle X}
55:{\displaystyle X}
37:Banach–Mazur game
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301:winning strategy
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25:topological game
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382:Further reading
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42:Given a subset
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402:(3): 316–329.
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374:, p. 116.
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27:introduced by
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360:(2): 227–276.
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297:countable set
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40:
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34:
33:Scottish book
30:
29:Stefan Banach
26:
22:
399:
393:
372:Mauldin 1981
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357:
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321:
315:
274:
64:real numbers
41:
20:
18:
21:Banach game
307:References
145:such that
228:∞
213:∑
192:⋯
133:…
421:Category
362:at 242.
328:
350:(PDF)
295:is a
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326:ISBN
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358:17
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