# 高微筆記(已停修)
###### tags: `高微`

筆記一覽
---

+ <a href = "https://hackmd.io/@Mes/High_Danger_Pre"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30> 前言 </a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_1"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30> Field 複習 </a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_2"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30> 數學歸納法與數列 </a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_3"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30> 收斂數列的性質、單調數列 </a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_4"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30> 集合的上下界、 cluster points</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_5"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30> cluster points、柯西數列</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_6"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30> 柯西數列的有界性、收斂性，有序體的 LUBP、MSP、BWP</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_7"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30> 實數完備性、數列發散到正負無窮的定義、上極限與下極限</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_8"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30> 上下極限與 cluster point、n 維歐氏空間的定義</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_9"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30> 賦範向量空間、矩陣的 norm</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_10"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>向量空間、內積空間、賦矩空間、柯西不等式</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_11"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>賦距空間中的收斂、極限唯一、有界性及 R^n 中的 BWP</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_12"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>數列之 cluster points、Banach 空間、絕對收斂、六個極限審練法</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_13"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>六個級數審斂法的證明、集合的極限點、內點以及閉包與內部</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_14"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>閉包、稠密性、集合邊界定義、閉集合</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_15"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>完備子空間、開集合、discrete metric space 的特例</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_16"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>Compact、Heine-Borel 定理、totally bounded 的定義與其有界性</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_17"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>Compact set</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_18"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>Pre-compact、sub-metric space 下的開集合與閉集合</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_19"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>在子空間中的閉集合、open relative to N ，accumulation points、derived set、函數極限的定義與唯一性、函數極限等價定義</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_20"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>函數極限存在的等價性質、函數的連續性</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_21"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>連續函數將 compact set 映到 compact set 以及將 connected set 映到 connected set 的證明</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_22"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>有限維賦範空間中的 compact、closed and bounded、兩個 norm 等價，BWP 和完備性</a>

+ <a href = "https://hackmd.io/@Mes/High_Danger_23"><img src = "https://i.imgur.com/thmVmX6.png?w=720" height = 30>函數之均勻連續性</a>

{%hackmd aPqG0f7uS3CSdeXvHSYQKQ %}

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