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

Let $f:\mathbb{R^n}\to \mathbb{R}$. If $G_f$ is the graph of $f$ and $G_f$ is closed, does it imply that $f$ is bounded?

share|cite|improve this question
Before you ask: Closedness of the graph does not even imply continuity, though that would at least be an implication that one might expect. – Hagen von Eitzen Mar 2 '13 at 14:53

No. Take $$ f:(x_1,\ldots,x_n)\longmapsto x_1. $$

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.