Open Subsets of LF-spaces

Kotaro Mine, and Katsuro Sakai. "Open Subsets of LF-spaces." Bulletin of the Polish Academy of Sciences. Mathematics 56.1 (2008): 25-37. <http://eudml.org/doc/281172>.

@article{KotaroMine2008,
abstract = {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 $ℝ^∞ = ind lim ℝ ⁿ$ (hence the product of an open subset of ℓ₂(τ) and $ℝ^∞$). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.},
author = {Kotaro Mine, Katsuro Sakai},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {classification of open sets; LF-space; density; open set; direct limit; ; -manifold},
language = {eng},
number = {1},
pages = {25-37},
title = {Open Subsets of LF-spaces},
url = {http://eudml.org/doc/281172},
volume = {56},
year = {2008},
}

TY - JOUR
AU - Kotaro Mine
AU - Katsuro Sakai
TI - Open Subsets of LF-spaces
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2008
VL - 56
IS - 1
SP - 25
EP - 37
AB - 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 $ℝ^∞ = ind lim ℝ ⁿ$ (hence the product of an open subset of ℓ₂(τ) and $ℝ^∞$). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.
LA - eng
KW - classification of open sets; LF-space; density; open set; direct limit; ; -manifold
UR - http://eudml.org/doc/281172
ER -