Displaying similar documents to “Autohomeomorphism groups of 0 -dimensional spaces”

Homomorphic images of ℝ -factorizable groups

Mihail G. Tkachenko (2006)

Commentationes Mathematicae Universitatis Carolinae

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It is well known that every ℝ -factorizable group is ω -narrow, but not vice versa. One of the main problems regarding ℝ -factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every ω -narrow group is a continuous homomorphic image of an ℝ -factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an ℝ -factorizable...