同学们大家好 我是复变(王教授班)的助教 由於蛮多同学来问我小考的是非题的答案 所以在此公布一下是非题的答案 1. The isolated points of a set form a closed set. False. A counterexample S = {i/n ; n = 1,2,3...}, all points are isolated points, but zero is a boundary point not in S. 3. The empty set is not an open set, and so it is a closed set. False. The empty set is not only an open set, but also a clolsed set. 4. It is impossible to have a neighborhood of x, N(x), that every point in N(x) is a boundary point of some set S. False. A counterexample; Set S are all rational number in [0,1]. All points of S are the boundary point of set S. 5. If Cauchy-Riemann equations are satisfied for f (z) = u(x,y)+iv(x,y) and u,v ∈ C^1 at a point z, then the function f (z) is analytic at z. False. At neighborhood of z. 祝同学考试顺利 加油~ --

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