Picture attached.
I expect any kind of help. Even hint or the first step.
Anyway, here is what I got
1. Clearly is always true, even when is not open. Let , and an open neighborh. of . It necessarily meets a point of , say . As , and is a neighborhood of , . So .
2. We consider the real line with usual topology, and . The LHS is but the RHS is empty.
What are some good books for a layperson who wants to teach himself set theory?
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