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Igor Belegradek
Igor Belegradek
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Let $U$ be the complement of a closed star-shaped subset in a separable infinite-dimensional Frechet space. Since every separable Frechet space is homeomorphic to $l_2$, one knows that $U$ is a Hilbert manifold.

Question: what else can be said about the topology of $U$? For example, is $U$ acyclic?

Let $U$ be the complement of a closed star-shaped subset in a separable infinite-dimensional Frechet space. Since every separable Frechet space is homeomorphic to $l_2$, one knows that $U$ is a Hilbert manifold.

Question: what else can be said about the topology of $U$? For example, is $U$ acyclic?

Let $U$ be the complement of a closed star-shaped subset in a separable infinite-dimensional Frechet space. Since every separable Frechet space is homeomorphic to $l_2$, one knows that $U$ is a Hilbert manifold.

Question: what else can be said about the topology of $U$?

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Igor Belegradek
Igor Belegradek
  • 29.1k
  • 2
  • 80
  • 176

Complement of a closed star-shaped subset in a Frechet space

Let $U$ be the complement of a closed star-shaped subset in a separable infinite-dimensional Frechet space. Since every separable Frechet space is homeomorphic to $l_2$, one knows that $U$ is a Hilbert manifold.

Question: what else can be said about the topology of $U$? For example, is $U$ acyclic?