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Table of Contents
Xingjian Tao's Notes and Question List
Notes
I made some notes on LaTex. You can see the PDF here math104_notes.pdf. The organization of definitions and theorems is mainly based on Rudin, though supplemented by Ross. Sometimes I tried to rewrite the contents in a more symbolic way, so there maybe minor mistakes.
Question List
1. How is the definition of limit points related with the concept of limit?
Answer: An element is a limit point of $E$ iff. it is the limit of some inconstant sequence of points in $E$. Inconstant is important because the definition of limit points includes hollow neighborhoods.
2. Suppose $E$ is an infinite subset of a set $K$. Then $E$ has a limit point in $K$ iff. $K$ is compact. Prove this.
Answer: $\Longrightarrow$ can be found in 2.37 Theorem of Rudin. $\Longleftarrow$ can be found in Excercise 26 of Rudin Chapter 2.
