0
$\begingroup$

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?

  • 1
    W should $b$e non-empty!2012-12-07

1 Answers 1

1

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.

  • 0
    If you mean to as$k$ 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.2012-12-08