Re: pathwise connection

On Jul 8, 4:03 pm, Sonya84 <sonianard...@xxxxxxxxx> wrote:

Sonya84 <sonianard...@xxxxxxxxx> writes:
Let H be an infinite dimensional Hilbert space.
Is GL(H) pathwise-connected ?

[snip Dr. Israel's suggestion of polar decomposition]

I know that GL(H) is contractible.

Hi, Sonya84:

Contractible means that the identity map is
homotopic to a constant map, so it's pretty
easy to show this implies path-connectedness
(consider the trajectories of points under
the homotopy mapping, all arriving at the
same constant endpoint).

regards, chip

.

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