Equivalent Metric Lemma

Hölder’s Inequality

Minkowski Inequality

P-Norm are equivalent on $\mathbb{R}^n$

Bolzano Weierstrass Theorem

Limit Superior 性質

Interior of A is the Largest Open Subset of A

Still Open Under Equivalent Metric

Closed Set and Closure 與 Set of Accumulation Points 之關係

Dense Subset 之充要條件

Cauchy Sequence is Bounded

R^n 是 Complete Metric Space

Reduced Complete Metric Space

(Sequentially) Compact then Bounded and Closed

(Sequentially) Compact then Totally Bounded

Compact 等價 Sequentially Compact