1. Math
  2. Advanced Math
  3. number 8...

Question: number 8...

Question details

Answer all items of the following problem: Consider the closed unit interval 1[o, 1] with its usual topology ui, see Definition 5.4, page 33. Let J [2, 3]. Define fJby f(r)-+2 Observe that f is a bijective function. Let X-IUJ For each a E J, let 3() ((x]). For each r e I, let B(r) (wu ((w)(f(x)): EWeu For example, 0 I and 0 [O, ) eu. Since f([o,) 2, 2) and f(0) 2, then [O, bu(12, 24)1 (2))-o, t (2, 23) B(o). Another example, consider E 1. We have 3) e ur. Also f((3 (2, 23) and f)2 Thus (u(f(()()))U (21,21)U(2),2) is a basic open neighborhoodof 1、That is,( 3 2) U ( 2h 32)U (2h, E293( ).

7. Prove that (X, T) is T2. 8. Evaiuate, with proof, each of the foliowing: (a) C( )neN. rint: To make your proof short, use part (7) above. (o) C(an InEN, where an- for each n e N. n+1

number 8

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution