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Ali Taghavi
Ali Taghavi
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Assume that $V$ is a finite dimensional real or complex normed linear space. Let $Iso(V)\subset GL(V)\subset L(V)$ be the space of linear isometric endomorphisms, invertible endomorphism and linear endomorphisms on $V$, respectively. These space have their natural and unique topologies, arising from the operator norm on $L(V)$.

Is $Iso(V)$ a deformation retract of $GL(V)$?

Assume that $V$ is a finite dimensional real or complex normed linear space. Let $Iso(V)\subset GL(V)\subset L(V)$ be the space of linear isometric endomorphisms, invertible endomorphism and linear endomorphisms on $V$. These space have their natural topologies,

Is $Iso(V)$ a deformation retract of $GL(V)$?

Assume that $V$ is a finite dimensional real or complex normed linear space. Let $Iso(V)\subset GL(V)\subset L(V)$ be the space of linear isometric endomorphisms, invertible endomorphism and linear endomorphisms on $V$, respectively. These space have their natural and unique topologies arising from the operator norm on $L(V)$.

Is $Iso(V)$ a deformation retract of $GL(V)$?

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Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

Is $Iso(V)$ a deformation retract of $GL(V)$ when $V$ is a finite dimensional linear normed space

Assume that $V$ is a finite dimensional real or complex normed linear space. Let $Iso(V)\subset GL(V)\subset L(V)$ be the space of linear isometric endomorphisms, invertible endomorphism and linear endomorphisms on $V$. These space have their natural topologies,

Is $Iso(V)$ a deformation retract of $GL(V)$?