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Every zero-dimensional space is cell soluble

Author: Toshiji Terada
Journal: Proc. Amer. Math. Soc. 110 (1990), 569-571
MSC: Primary 54C99; Secondary 54F45
MathSciNet review: 1021906
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Abstract: In his study of the question of representing a space as a retract of a homogeneous space, Arhangel'skii introduced an interesting topological property called cell solubility. He raised the following problem: Is every zero-dimensional compact space cell soluble? We will give an affirmative answer to this problem.

References [Enhancements On Off] (What's this?)

  • [1] A. V. Arhangel'skii, Cell structures and homogeneity, Mat. Zametki 37 (1985), 580-586; Math. Notes 37 (1985), 321-324. MR 790982 (87a:54037)
  • [2] -, Topological homogeneity. Topological groups and their continuous images, Uspekhi Mat. Nauk 2 (1987), 69-105; Russian Math. Surveys 2 (1987), 83-131. MR 898622 (89b:54004)
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Keywords: Homogeneous, zero-dimensional, retract, cell soluble
Article copyright: © Copyright 1990 American Mathematical Society

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