1. Let A,B,C, and D be subsets of R^2 (with the usual Euclidean metric).
下列三種情形,是否正確?為什麼? If it is always true, prove it.
If it can be false, give a counterexample.
(a.) If C ⊆ D, then cl(C) ⊆ cl(D)
(b.) cl(A∩B) ⊆ cl(A)∩cl(B)
(c.) A ⊆ cl(int(A))
2. Suppose f:R→R and that |f(x)-f(y)| <= 5|x-y| for all x and y in R.
Show that f is continuous on R.
3. Find a number b such that the function from R to R defined by
x^2 - 9
--------- for x≠3
╭ x - 3
f(x) = │
╰ b for x=3
is continuous.
麻煩各位的指教了！ 謝謝!
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