Past exam of the options II course of the University of Oxford / 2012 / E / E3 / b / ii / 2

Table of contents
- Solution 2

Solution

Take

A_{2} = {(1/ n, 0) : n \geq 1} .

(1)

Its only accumulation point is

(0, 0)

, which is absent from

A_{2}

. Every listed point is isolated, so none belongs to

A_{2}^{'}

. Consequently

A_{2}^{'} = {(0, 0)}, A_{2}^{'} \neq \subseteq A_{2}, A_{2} \neq \subseteq A_{2}^{'} .

(2)

For completeness, away from the origin a sufficiently small disk meets only finitely many of the listed points and can be shrunk to exclude all but its centre, proving there are no further accumulation points.

 Ancestors (14)

ii
b
E3
E
2012
Past exam of the options II course of the University of Oxford
Options II course of the University of Oxford
Year 2 of the mathematics course of the University of Oxford
Mathematics course of the University of Oxford
Undergraduate course of the University of Oxford
Course of the University of Oxford
University of Oxford
List of universities
 Home

 View article source

 Discussion (0) New discussion

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

Past exam of the options II course of the University of Oxford / 2012 / E / E3 / b / ii / 2

Solution

 Ancestors (14)

 Discussion (0)  Subscribe (1) New discussion

 Articles by others on the same topic (0)

 Discussion (0) New discussion