Does anybody have a good resource with worked solutions for quick revision of some basic results from analysis? I am self-studying a maths course on Fixed-Point Theorems (Course notes here) over the summer. I've just finished the first section, which covers some basic results from analysis such as
- Vectors and Norms
- Convergence
- Multidimensional Bolzano-Weierstrass Theorem
- Basic Properties of Open and Close sets
- Basic Definitions of continuity
- The Multidimensional Extreme Value Theorem
- The Glueing Lemma
- Lebesgue Numbers
I'm familiar with these concepts from past modules that covered these topics and others in some depth but I'm just a bit rusty after taking a bit of time off college. I would like to do some simple problems that use these concepts just to make sure I'm comfortable using them.
If you know of a resource with a few practice problems with worked solutions for these concepts it would be greatly appreciated. Especially if the resource is designed for mathematical economics or is oriented toward building the basics for Brouwers Fixed Pointy Theorem.
Thanks in advance for any help!