* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Exercises
Survey
Document related concepts
Transcript
Advanced Analysis Spring 2006 Exercises for Feb 1st: E1: Let S be a topological space. We say that S is connected if it cannot be decomposed as a union of two nonempty disjoint open sets. A subset of S is called clopen if it is both open and closed. Show that S is connected if and only if S and ∅ are the only clopen sets in S. E2: Let S be a topological space. If A ⊆ S and x ∈ S then x ∈ A if and only if A ∩ N 6= ∅ for every neighborhood N of x. 1