Products and h-homogeneity |
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Authors: | Andrea Medini |
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Institution: | Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USA |
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Abstract: | Building on work of Terada, we prove that h-homogeneity is productive in the class of zero-dimensional spaces. Then, by generalizing a result of Motorov, we show that for every non-empty zero-dimensional space X there exists a non-empty zero-dimensional space Y such that X×Y is h-homogeneous. Also, we simultaneously generalize results of Motorov and Terada by showing that if X is a space such that the isolated points are dense then Xκ is h-homogeneous for every infinite cardinal κ. Finally, we show that a question of Terada (whether Xω is h-homogeneous for every zero-dimensional first-countable X) is equivalent to a question of Motorov (whether such an infinite power is always divisible by 2) and give some partial answers. |
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Keywords: | h-Homogeneous Clopen set Pseudocompact Zero-dimensional First-countable Homogeneous Infinite power |
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