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Continuous functions-(1)

3 minute read

Definition 4.2.1 $f:E\to \mathbb{R}$ is continuous at $p\in E$, if $\forall \epsilon >0, \exists \delta >0$ such that $|x-p|<\delta \Rightarrow |f(...

Group and Ring

4 minute read

Definition 1 $\cdot: G\times G \to G$ is binary operation where we write $x\cdot y =xy$ for $x,y\in G$. $(G,\cdot)$ is group if it satisfies the followings ...

Limit of function

6 minute read

4.1.1 Definition $E \subset \mathbb{R}, f: E \rightarrow \mathbb{R}$: a function, $p \in E^\prime$. $f$ has a limit at p if there exists $L\in \mathbb{R}$ su...

Cantor Set

4 minute read

Definition of Cantor Set For each $P_i$ is non empty compact set and $P_0 \supset P_1 \supset P_2 \cdots$. Define $P$ as follows: \(\begin{align} P := \cap_{...

Compact set

10 minute read

Theorem 3.2.5 (a) $K$ is compact $\Rightarrow$ $K$ is closed and bounded