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The weight of lexicographic products

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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… Click to show full abstract

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 .

Keywords: assertion; weight lexicographic; product; topology; lexicographic products

Journal Title: Topology and its Applications
Year Published: 2020

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