9.9. Notes

9.9.1. Online examples

Result

Let \(X\) be an infinite set and \(\mathrm{T}\) a topology on \(X\). If every infinite subset of \(X\) is in \(\mathrm{T}\), prove that \(\mathrm{T}\) is the discrete topology.

http://math.stackexchange.com/questions/60269/question-regarding-subsets-of-infinite-sets

Result

Show that all open intervals (a,b) in \(\mathbb{R}\) are \(F_\sigma\) sets.

http://math.stackexchange.com/questions/179808/show-that-any-open-subsets-of-the-real-line-are-f-sigma-sets

• Proof of Baire Category Theorem

9.9.2. References

• Sketches of topology