I was looking for some material that could help me understand a real analysis course (1st year undergraduate). My teacher treated the following topics:
Partition of unity
Existence of regular functions on compact support
Dyadic covering and Paley Littlewood's partition of unit.
Morse's lemma.
Do you know any book or note where I can find a simple introduction to these topics?
Thank you!
Shifrin's differential geometry notes contain most of those and are free on the web. math.uga.edu/~shifrin/ShifrinDiffGeo.pdf