On Buzyakova's example; quotients of the Cantor trees |
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Authors: | Lei Mou |
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Institution: | Mathematics Department, Capital Normal University, Beijing 100037, China |
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Abstract: | Let T be the Cantor tree and let A be a subset of the ωth level of T (= Cantor set C). Buzyakova considered the quotient space TAT′ obtained from T×2 by identifying two points 〈a,0〉 and 〈a,1〉 for each a∈A to construct an example of a non-submetrizable space of countable extent with a Gδ-diagonal. We prove that the space TAT′ is submetrizable if and only if C?A is an Fσ-set in C with the Euclidean topology. This improves Buzyakova's Lemma. |
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Keywords: | 54B15 54E99 |
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