Abstract We will calculate the weight of lexicographic products of GO-spaces, using this we will see: • the assertion that the weight of the lexicographic product 2 ω 1 is ℵ 1 is equivalent to the Continuum Hypothesis (CH), that is, 2 ℵ 0 = ℵ 1 , • the assertion that the weight of both lexicographic products 2 ω 1 and 2 ω 1 + 1 coincide is equivalent to the assertion 2 ℵ 0 = 2 ℵ 1 , • the assertion that the lexicographic product 2 γ is homeomorphic to the usual Tychonoff product 2 γ is equivalent to γ ≤ ω .

中文翻译：

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词典产品权重

摘要 我们将计算 GO 空间的词典产品的权重，使用它我们将看到： • 词典产品 2 ω 1 的权重为 ℵ 1 的断言等价于连续统假设 (CH)，即 2 ℵ 0 = ℵ 1 , • 两个字典积 2 ω 1 和 2 ω 1 + 1 的权重一致的断言等价于断言 2 ℵ 0 = 2 ℵ 1 , • 字典积 2 γ 是同胚的断言到通常的 Tychonoff 乘积 2 γ 等价于 γ ≤ ω 。