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Annotation system

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Reasoning

Digital keyboard

Kanbun-LM is not shown here because automatic generation is Japanese-only. This patch keeps the manual path as the default workflow.

Source page


# WORK_TITLE: 拓撲學
# DISPLAY_TITLE: 拓撲學
# AUTHOR:
# TIMES:
# PAGE_TITLE: 拓撲學
# CATEGORIES:
拓撲學，亦曰
位相學，
幾何學
引伸也，論物之形，毋視度量，故亦曰「橡膠幾何」。

拓撲學之心，
拓撲空間
也。拓撲空間之研究，曰「點集拓撲」；加諸般條件，因以代數方法論之，曰「代數拓撲」；至若加諸般條件，因以分析方法論之，曰「微分拓撲」。

三角及方圓，咸二分平面，無限、有限各一，故以拓撲學觀之，此三物同形也。符號若「日」、「８」、「呂」者，三分平面，無限一而有限二，故亦同形也。由此可見，橡膠幾何之由也。

史

一七三六年，
歐拉
解
七條橋問題，橋之長度位置，槪不理會，譽拓撲學之始。然拓撲學一詞，始於一八四七年，意無視量度之幾何。一八九八年，
龐加萊
究
同構，為「代數拓撲」之始。

一九零六年，
莫里斯·弗雷歇
一統
函數
空間之研究，創
度量空間
。一九一四年，
豪斯多夫
引入「拓撲」一詞，所修之拓撲空間，今曰
豪斯多夫空間
。

當世「拓撲空間」之定義，乃
庫拉托夫斯基
於一九二二年所定。

註

拓撲術語

拓撲
｜

子空間
｜

積空間
｜

商空間
｜

拓撲分類
｜

點
｜

內
｜

外
｜

極限點
｜

孤點
｜

周界
｜

曲線
｜

道路
｜

開集
｜

閉集
｜

閉包
｜

閉開集
｜

分離
｜

稠密
｜

度量
｜

距
｜

有界
｜

鄰域
｜

覆蓋
｜

緊集
｜

連通
｜

道路連通
｜

單連通
｜

局部
｜

基
｜

準基
｜

連續
｜

開函數
｜

閉函數
｜

同胚
｜

同倫
｜

拓撲不變量

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Punctuation options

Preset Source Modern CJK (Traditional) Modern CJK (Simplified / PRC) Pure classical Strip Custom

Quotes

Family

Chinese quotation marks 「」『』 Latin speech marks “ ” ‘ ’ Chinese speech marks ＂＇ Off

Ordering

Traditional: 「甲『乙』丙」 Simplified: 『甲「乙」丙』 Vertical quote forms (﹁﹂﹃﹄)

Question / Exclamation Keep ？ Collapse ? → 。

Keep ！ Collapse ! → 。

Semicolon / Colon Keep ； Collapse ; → 。

Keep ： Collapse : → 。

Comma Use ， Use 、

Repetition mark No repetition mark (default) 々 (Horizontal) 〻 (Vertical) 二 (Western Zhou-style)

# WORK_TITLE: 拓撲學 # DISPLAY_TITLE: 拓撲學 # AUTHOR: # TIMES: # PAGE_TITLE: 拓撲學 # CATEGORIES: 拓撲學，亦曰位相學，幾何學引伸也，論物之形，毋視度量，故亦曰「橡膠幾何」。拓撲學之心，拓撲空間也。拓撲空間之研究，曰「點集拓撲」；加諸般條件，因以代數方法論之，曰「代數拓撲」；至若加諸般條件，因以分析方法論之，曰「微分拓撲」。三角及方圓，咸二分平面，無限、有限各一，故以拓撲學觀之，此三物同形也。符號若「日」、「８」、「呂」者，三分平面，無限一而有限二，故亦同形也。由此可見，橡膠幾何之由也。史一七三六年，歐拉解七條橋問題，橋之長度位置，槪不理會，譽拓撲學之始。然拓撲學一詞，始於一八四七年，意無視量度之幾何。一八九八年，龐加萊究同構，為「代數拓撲」之始。一九零六年，莫里斯·弗雷歇一統函數空間之研究，創度量空間。一九一四年，豪斯多夫引入「拓撲」一詞，所修之拓撲空間，今曰豪斯多夫空間。當世「拓撲空間」之定義，乃庫拉托夫斯基於一九二二年所定。註拓撲術語拓撲｜子空間｜積空間｜商空間｜拓撲分類｜點｜內｜外｜極限點｜孤點｜周界｜曲線｜道路｜開集｜閉集｜閉包｜閉開集｜分離｜稠密｜度量｜距｜有界｜鄰域｜覆蓋｜緊集｜連通｜道路連通｜單連通｜局部｜基｜準基｜連續｜開函數｜閉函數｜同胚｜同倫｜拓撲不變量