1. Let S be any subset of the real numbers. Prove that int( S ) is open. Prove that S is open if and only if S = int( S ). 首先看内点的定义是：A point s S is called interior point of S if there exists a neighborhood of S completely contained in S . 所有内点的集合是 int ( S ). ...
Is the set { x R : | x | 1, x^= 0 } connected or disconnected ? The first set is open, so we can try to use the easier definition of disconnected. It is indeed disconnected; it can be 'split at 0'. More precisely, let U = (-1,0) and V = (0,1). Then U and V have emp ...
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