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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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Propose a text edit (creates a ticket)

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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