Corpus Viewer

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Create annotation system (creates a ticket)

Manual annotation is the default. Approved files are written as sibling pages under kanbun/, hanmun/, or hanvan/ with the same filename as this source page.

Annotation system

Summary

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: 單連通
# DISPLAY_TITLE: 單連通
# AUTHOR:
# TIMES:
# PAGE_TITLE: 單連通
# CATEGORIES:
註蓋當今數學之事，誠難僅以文述，而無符號，故凡數學之文，咸有漢字、拉丁字相易之事，以合文言、數學，則無論文理之人，皆可明之也。

單連通者，無洞也，反之曰多連通
。

定義

道路連通集曰單連通者，凡圈
咸同倫常數也（即可縮作一點），同乎其同倫群為零，故又曰一連通也。

單通連之面，其虧格為零。

單通連乃拓撲不變量也。

例

平面，單連通也。平面去一點，非單連通也。高維歐几里德空間去一點，單連通也。

圓，非單連通也。高維球，單連通也。

環狀，非單連通也。

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

Annotation-system text

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References

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AI assistance disclosure

AI-assisted What was assisted?

Evidence links

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Evidence files

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Optional contact details

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Save this ticket key on this device

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Ticket ID:

Ticket key (save this): Open ticket

Add companion material (creates a ticket)

Approved material appears beside this corpus text. The 20 MB limit applies to this submission only; the text may accumulate any number of approved submissions.

Material type

Optional edition or material label

Translations are identified in menus by language and translator, not by this label.

Translation language (ISO 639-3)

The stored value is the selected three-letter ISO 639-3 code.

Translator

Leave blank for anonymous or unidentified translations.

Translation text

Material files

PNG, JPEG, or PDF. Together with evidence files, this ticket may contain up to 10 files and 20 MB.

Related corpus path

Material links

Ticket summary

Reviewer reasoning

Material note *

Provenance *

Choose every label that applies. At least one is required.

User-made Public domain Historical source or manuscript Author-provided: the work's author supplied this translation

References

A formal citation style is welcome but not required.

AI assistance disclosure

AI-assisted What was assisted?

Evidence links

Links are preferred when the evidence already exists online.

Evidence files

Up to 10 files and 20 MB for this ticket. HTML, XHTML, and SVG are rejected.

Optional contact details

Stored separately and encrypted. Deleted after 30 days or when the ticket closes.

Name Email Contact note

Save this ticket key on this device

Unchecked by default. The key is otherwise shown once and is not stored by the browser.

Ticket ID:

Ticket key (save this):

Propose a text edit (creates a ticket)

This does not change the corpus directly. It creates a ticket with a unified diff attached.

Title

Summary

Reasoning

Edited text

Evidence links

Links are preferred when the evidence already exists online.

Evidence files

Up to 10 files and 20 MB for this ticket. HTML, XHTML, and SVG are rejected.

Optional contact details

Stored separately and encrypted. Deleted after 30 days or when the ticket closes.

Name Email Contact note

Save this ticket key on this device

Unchecked by default. The key is otherwise shown once and is not stored by the browser.

Ticket ID:

Ticket key (save this):

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: 單連通 # DISPLAY_TITLE: 單連通 # AUTHOR: # TIMES: # PAGE_TITLE: 單連通 # CATEGORIES: 註蓋當今數學之事，誠難僅以文述，而無符號，故凡數學之文，咸有漢字、拉丁字相易之事，以合文言、數學，則無論文理之人，皆可明之也。單連通者，無洞也，反之曰多連通。定義道路連通集曰單連通者，凡圈咸同倫常數也（即可縮作一點），同乎其同倫群為零，故又曰一連通也。單通連之面，其虧格為零。單通連乃拓撲不變量也。例平面，單連通也。平面去一點，非單連通也。高維歐几里德空間去一點，單連通也。圓，非單連通也。高維球，單連通也。環狀，非單連通也。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