منابع مشابه
Banach-Mazur Games on Graphs
We survey determinacy, definability, and complexity issues of Banach-Mazur games on finite and infinite graphs. Infinite games where two players take turns to move a token through a directed graph, thus tracing out an infinite path, have numerous applications in different branches of mathematics and computer science. In the usual format, the possible moves of the players are given by the edges ...
متن کاملMazur-Ulam Theorem
The notation and terminology used in this paper have been introduced in the following papers: [19], [18], [4], [5], [20], [11], [10], [14], [17], [1], [6], [16], [24], [25], [21], [13], [12], [22], [2], [9], [8], [3], and [7]. For simplicity, we use the following convention: E, F , G are real normed spaces, f is a function from E into F , g is a function from F into G, a, b are points of E, and...
متن کاملMazur-Ulam Theorem
The notation and terminology used in this paper have been introduced in the following papers: [19], [18], [4], [5], [20], [11], [10], [14], [17], [1], [6], [16], [24], [25], [21], [13], [12], [22], [2], [9], [8], [3], and [7]. For simplicity, we use the following convention: E, F , G are real normed spaces, f is a function from E into F , g is a function from F into G, a, b are points of E, and...
متن کامل2 Separating Hyperplanes 3 Banach–mazur Distance
We’ll use the above result to show why the polar of the polar of a convex body is the body itself. Recall that for a convex body K, we had defined its polar K∗ to be {p|k · p ≤ 1∀k ∈ K}. Theorem 2 Let K be a convex body. Then K∗∗ = K. Proof We know that K∗ = {p|k · p ≤ 1∀k ∈ K}. Similarly K∗∗ = {y|p · y ≤ 1∀p ∈ k∗}. Let y be any point in K. Then, by the definition of the polar, for all p ∈ K∗ w...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1969
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700041411