Mahler's compactness theorem
In mathematics, Mahler's compactness theorem, proved by Kurt Mahler , is a foundational result on lattices in Euclidean space, characterising sets of lattices that are 'bounded' in a certain definite sense. Looked at another way, it explains the ways in which a lattice could degenerate (go off to infinity) in a sequence of lattices. In intuitive terms it says that this is possible in just two ways: becoming coarse-grained with a fundamental domain that has ever larger volume; or containing shorter and shorter vectors. It is also called his selection theorem, following an older convention used in naming compactness theorems, because they were formulated in terms of sequential compactness (the possibility of selecting a convergent subsequence).
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Mahler's compactness theorem
In mathematics, Mahler's compactness theorem, proved by Kurt Mahler , is a foundational result on lattices in Euclidean space, characterising sets of lattices that are 'bounded' in a certain definite sense. Looked at another way, it explains the ways in which a lattice could degenerate (go off to infinity) in a sequence of lattices. In intuitive terms it says that this is possible in just two ways: becoming coarse-grained with a fundamental domain that has ever larger volume; or containing shorter and shorter vectors. It is also called his selection theorem, following an older convention used in naming compactness theorems, because they were formulated in terms of sequential compactness (the possibility of selecting a convergent subsequence).
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In mathematics, Mahler's compa ...... Mumford's compactness theorem.
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数学におけるマーラーのコンパクト性定理(マーラーのコンパクト ...... れた。詳しくはマンフォードのコンパクト性定理を参照されたい。
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965,663,129
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Kurt Mahler
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Kurt
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Mahler
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In mathematics, Mahler's compa ...... ing a convergent subsequence).
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数学におけるマーラーのコンパクト性定理(マーラーのコンパクト ...... なるものが存在するため、この函数は剰余類の上では定数となる。
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Mahler's compactness theorem
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マーラーのコンパクト性定理
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