# Some series convergence problems

Here are some series convergence problems that I gathered quite a while ago. A few of them are a bit tricky.

# Every continuous open mapping of R into R is monotonic

I’m willing to bet that most students who have used Rudin’s Principles of Mathematical Analysis have encountered this problem: 15. Call a mapping of $$X$$ into $$Y$$ open if $$f(V)$$ is an open set in $$Y$$ whenever $$V$$ is an open set in $$X$$. Prove that every continuous open mapping of $$\mathbb{R}$$ into $$\mathbb{R}$$ is […]