1) True or false: (With explanations) a) Every boundary point of a set is an acc

Question

1) True or false: (With explanations) a) Every boundary point of a set is an accumulation point of that set b) If a the points of a set A are accumulation points, then A must be closed. c) If a the points of a set A are isolated, then A must be closed d) If a set contains all its interior points, then it must be open. 2) Let A R B. Show that an interior point of B cannot be an accumulation point of A 3) Let E be a set and n a sequence of elements in E. Suppose that lim Tn -T and that r is an isolated point of E. Show that there is an integer N so that n r for all n N. 4) Give an example of a subset E of R that has no accumulation points, but that satisfies the property that for everve > 0, there exists points 2, y E E so that O

Explanation / Answer

example 1. (trivial example) let, E = , the empty set, then E has no limit (accumulation) points, i.e. the derived set of E denoted by E' =

but, for all x,y in E anf for any > 0 we have vacously, 0 < |x-y| <

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.