by Daniel
Last Updated January 12, 2018 20:20 PM

Suppose we have two sets in R^n, C and D, with C being closed and D being open. We are asked to prove that the set C\D is closed.

However, if we consider the complement of D\C, we get the intersection of C and the complement of D. But, since D is open, it must be that the complement of D is closed by definition. So, the complement of D\C is simply the intersection of two closed sets, so it must be closed. We then have that D\C must be open.

There clearly must be an error in my logic. Could someone hint me at where I'm going wrong?

- Serverfault Help
- Superuser Help
- Ubuntu Help
- Webapps Help
- Webmasters Help
- Programmers Help
- Dba Help
- Drupal Help
- Wordpress Help
- Magento Help
- Joomla Help
- Android Help
- Apple Help
- Game Help
- Gaming Help
- Blender Help
- Ux Help
- Cooking Help
- Photo Help
- Stats Help
- Math Help
- Diy Help
- Gis Help
- Tex Help
- Meta Help
- Electronics Help
- Stackoverflow Help
- Bitcoin Help
- Ethereum Help