(4) Q: Let T denote the collection of the empty set and all subsets of R...

Transcribed Image Text:

(4) Q: Let T denote the collection of the empty set and all subsets of R that contain the clement 0. (a) Prove 7 is a topology on R. (b) Find the interior of the rational numbers, Q, as a subset of (R, 7). (c) Find the interior of (1,5) as a subset of (R, 7). (d) Find the closure of [-1,2] as a subset of (R, T). (c) Find the closure of (1,5) as a subset of (R, 7). (4) Q: Let T denote the collection of the empty set and all subsets of R that contain the clement 0. (a) Prove 7 is a topology on R. (b) Find the interior of the rational numbers, Q, as a subset of (R, 7). (c) Find the interior of (1,5) as a subset of (R, 7). (d) Find the closure of [-1,2] as a subset of (R, T). (c) Find the closure of (1,5) as a subset of (R, 7).

Answer rating: 100% (QA)

2 b Since oeB So B is an often set of R2 interior B Therefore Since ... View the full answer