Past exam of the mathematics course of the University of Cambridge / 2014 / ib / Paper 2 / 12F / ii

Table of contents
- Solution ii

Solution

True. The same subsequence argument applies to the sum of a compact set and a closed set. For a convergent sequence

z_{j} = x_{j} + y_{j}

, boundedness of

X

provides a convergent subsequence of

x_{j}

, with limit

x \in X

. Then

y_{j} \to z - x \in Y

along that subsequence. Consequently

z \in X + Y

. No boundedness of

Y

is needed.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version