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Consider the set $(-\infty, 0]\cup\{1/n:n\in\mathbb{N}\}$ with the subspace topology. Then

  1. $0$ is an isolated point
  2. $(–2, 0]$ is an open set
  3. $0$ is a limit point of the subset $\{1/n:n\in\mathbb{N}\}$
  4. $(–2, 0)$ is an open set.

I think 3 and 4 are correct.am I right?

  • 2
    Yes. Can you answer why you're right?2012-12-18

1 Answers 1