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 N be an open set of YxZ. Is there exist an open set W in YxZ with compact boundry such that W is a subset of N?

share|cite|improve this question
Yes, take $W$ to be empty. – Chris Eagle Dec 7 '12 at 18:58
W should be non-empty! – aliakbar Dec 7 '12 at 18:59

Not in general, no. For example, let $Y$ be an infinite set with the particular point topology, and $Z$ be a one-point space. Then $N=\{(p,*)\}$ (where $p$ is the particular point of $Y$ and $*$ is the only point of $Z$ is a counterexample.

share|cite|improve this answer
Is the your answer satisfies in a Hausdorff space? – aliakbar Dec 8 '12 at 4:36
If you mean to ask whether my example is Hausdorff, it isn't. If you mean to ask whether there's a Hausdorff example, I don't know. I expect so, though. – Chris Eagle Dec 8 '12 at 10:26

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.