Open Subsets of LF-spaces

• Autorzy: Kotaro Mine , Katsuro Sakai
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57N17: Topology of topological vector spaces
• 57N20: Topology of infinite-dimensional manifolds
• 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.)
• 46T05: Infinite-dimensional manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: 56
• Numer: 1
• Strony: 25-37

Daty

wydano

2008

Twórcy

autor

Kotaro Mine

• Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan

autor

Katsuro Sakai

• Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan

Identyfikatory

DOI

10.4064/ba56-1-4