Scattered countable metric spaces X for which X × X ≈ X

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概要

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• As an application of [2], we shall give a characterization of locally compact countable metric spaces X for which X × X ≈ X , namely X ≈ LC (ωγ) if leng (X) > 1. We shall also give 2ℵ0 many scattered countable metric spaces X for which X × X ≈ X. In a classical paper ([1]), Mazurkiewicz and Sierpiński counted the number of locally compact countable metric spaces and scattered countable metric spaces. The former was found to be ℵ1 and the latter to be 2ℵ0. We shall show that there are sufficiently many scattered countable metric spaces X for which X × X ≈ X. In a classical paper ([1]), Mazurkiewicz and Sierpiński counted the number of locally compact countable metric spaces and scattered countable metric spaces. The former was found to be ℵ1 and thelatter to be 2ℵ0. We shall show that there are sufficiently many scattered countable metric spaces X forwhich X × X ≈ X .

• 香川大学教育学部の論文
• 2009-10-30

著者

• 岡 晋平

  香川大学教育学部

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