Suppose that A and B are subsets of ℝ such that A is open and B is closed. Prove that A-B is open and B-A is closed. hint: use the fact that if X and Y are subsets of ℝthen X-Y=X∩(ℝ-Y). PLEASE SHOW ME THE LIGHT!!

Printable View

- Oct 28th 2008, 02:00 PMgatesamaticopen and closed sets proof
Suppose that A and B are subsets of ℝ such that A is open and B is closed. Prove that A-B is open and B-A is closed. hint: use the fact that if X and Y are subsets of ℝthen X-Y=X∩(ℝ-Y). PLEASE SHOW ME THE LIGHT!!

- Oct 28th 2008, 02:19 PMPlato
For set difference $\displaystyle A\backslash B = A \cap B^c \,\& \,B\backslash A = B \cap A^c$.

Recall that the complement of a closed set is an open set and the intersection of two open sets is an open set.

Recall that the complement of an open set is a closed set and the intersection of two closed sets is a closed set. - Oct 28th 2008, 04:07 PMgatesamatic
- Oct 28th 2008, 05:19 PMPlato
This is my own take on this.

These are questions about basic topology.

I do not think that topics in topology have any place in a course on*discrete mathematics.*

Your instructor gave you something beyond your grasp.

The sad truth is: it may enhance her/his on importance without doing anything for you.