Erdős space is the “rational” Hilbert space, that is, the set of vectors in ℓ² with all coordinates rational. Erdős proved that is one-dimensional and homeomorphic to its own square × , which makes it an important example in dimension theory. Dijkstra and van Mill found topological characterizations of . Let , n ∈ ℕ, be the n-dimensional Menger continuum in , also known as the n-dimensional Sierpiński carpet, and let D be a countable dense subset of . We consider the topological group of all autohomeomorphisms of that map D onto itself, equipped with the compact-open topology. We show that under some conditions on D the space is homeomorphic to for n ∈ ℕ ∖ 3.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm207-1-1,
author = {Jan J. Dijkstra and Dave Visser},
title = {Homeomorphism groups of Sierpi\'nski carpets and Erd\H os space},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {1-19},
zbl = {1193.57015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm207-1-1}
}
Jan J. Dijkstra; Dave Visser. Homeomorphism groups of Sierpiński carpets and Erdős space. Fundamenta Mathematicae, Tome 209 (2010) pp. 1-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm207-1-1/