Let $X $ be a compact non-Hausdorff topological space with the following property: for every infinite subset of closed points, say $\{x_i\}_{i \in I}$, there exists $j\in I$ such that $x_j$ is in the closure of $\{x_i\}_{i \not=j}$.

Is there any characterization of such spaces? Or is there any sufficient or necessary condition for this property? Thanks for any help.

  • 1
    $\begingroup$ You should edit your question to be clearer. $\endgroup$ – Chris Ramsey Dec 2 '15 at 17:26
  • $\begingroup$ I fixed up the grammar a little. To clarify, a "closed point" is a point $x$ such that $\{x\}$ is closed? $\endgroup$ – Nate Eldredge Dec 2 '15 at 17:32
  • 2
    $\begingroup$ Your edit reversed the changes I made; did you mean to do that? $\endgroup$ – Nate Eldredge Dec 2 '15 at 17:36
  • 1
    $\begingroup$ This looks rather like a homework exercise. What's the motivation for asking the question...? $\endgroup$ – Paul Levy Dec 2 '15 at 21:29

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.