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並前往https://math.unm.edu/~crisp/courses/math402/Math402-straugh/sol-hwk2.pdf

(p. 408) 12.3.1; (p. 411) 12.4.7. First let's prove t

In other words, E is open if and only if for every x ∈ E, there exists an r > 0 such that B(x, r) ⊆ E. (b) Let E be a subset of X. Then E is closed if and ...

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