Let F = ind lim Fₙ be an infinite-dimensional LF-space with density dens F = τ ( ≥ ℵ ₀) such that some Fₙ is infinite-dimensional and dens Fₙ = τ. It is proved that every open subset of F is homeomorphic to the product of an ℓ₂(τ)-manifold and (hence the product of an open subset of ℓ₂(τ) and ). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-1-4,
author = {Kotaro Mine and Katsuro Sakai},
title = {Open Subsets of LF-spaces},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {56},
year = {2008},
pages = {25-37},
zbl = {1181.46002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-1-4}
}
Kotaro Mine; Katsuro Sakai. Open Subsets of LF-spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) pp. 25-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-1-4/