Closed subset of a Hilbert space

Question

$Y_0\subset Y $ is a closed Hilbert subspace of $Y$ with finite codimension and a subspace $ Y_1 $ satisfies $ Y_0 \subset Y_1 \subset Y $. Is $ Y_1 $ also closed?

score 2 · Accepted Answer · answered Feb 03 '13 at 18:18

2

Consider $\pi(Y_1) \subset Y/Y_{0}$, noting that a set is closed in the quotient topology precisely when its inverse is closed in the original space.

answered Feb 03 '13 at 18:18

Elchanan Solomon

30,807

Closed subset of a Hilbert space

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