A conjecture of J. Nagata on dimension and metrization
A conjecture of J. Nagata on dimension and metrization
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J. Nagata关于维度和度量化的猜想
DOI：
10.1090/s0002-9904-1965-11364-7
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发表时间：
1965
影响因子：
1.3
通讯作者：
Phillip A. Ostrand
中科院分区：
文献类型：
--
作者：
Phillip A. Ostrand
在本文中，我们简要概述了 J. Nagata 猜想的定理 1 的证明 [l]。我们所说的维度总是指覆盖维度。如果 X 的每个点都有一个满足该族中最多一个成员的邻域，则 X 的子集族是离散的。对于 X 的子集 A 和 X 的子集族 6，令 S(A, <B) 表示 A 和所有那些 C £ 6 的并集，使得 CC\AT0。对于每个整数 w^O，让
In this paper we outline briefly a proof of Theorem 1, which was conjectured by J. Nagata [ l ] . By dimension we shall always mean covering dimension. A family of subsets of X is discrete if each point of X has a neighborhood which meets a t most one member of the family. For a subset A of X and a family 6 of subsets of X, let S(A, <B) denote the union of A and all those C £ 6 such that CC\AT0. For each integer w^O, let