Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$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?

share|cite|improve this question
up vote 2 down vote accepted

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.