開写像定理 (関数解析)

Open mapping theorem - Theorem that surjective continuous operators on Banach spaces are open maps. Article "開写像定理 (関数解析)" in Japanese Wikipedia has 4.1 points for quality (as of July 1, 2025). The article contains 0 references and 4 sections.

This article has the best quality in English Wikipedia. Also, this article is the most popular in that language version.

Since the creation of article "開写像定理 (関数解析)", its content was written by 6 registered users of Japanese Wikipedia and edited by 238 registered Wikipedia users in all languages.

The article is cited 54 times in Japanese Wikipedia and cited 669 times in all languages.

The highest Authors Interest rank from 2001:

• Local (Japanese): #43528 in July 2012
• Global: #29362 in April 2003

The highest popularity rank from 2008:

• Local (Japanese): #441709 in July 2022
• Global: #348003 in November 2021

There are 18 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

#	Language	Quality grade	Quality score
1	English (en) Open mapping theorem (functional analysis)		38.2481
2	French (fr) Théorème de Banach-Schauder		35.2076
3	Dutch (nl) Open afbeeldingsstelling		24.1695
4	Portuguese (pt) Teorema de Banach-Schauder		19.8301
5	Catalan (ca) Teorema de la funció oberta		16.4564
6	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		12.3309
7	Chinese (zh) 开映射定理		9.5885
8	Italian (it) Teorema della funzione aperta (analisi funzionale)		8.3339
9	Hebrew (he) משפט ההעתקה הפתוחה		5.1575
10	Swedish (sv) Satsen om den öppna avbildningen		4.934

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The following table shows the most popular language versions of the article.

The most popular language versions of the article "開写像定理 (関数解析)" in all the time

#	Language	Popularity award	Relative popularity
1	English (en) Open mapping theorem (functional analysis)		407 607
2	French (fr) Théorème de Banach-Schauder		82 419
3	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		52 401
4	Polish (pl) Twierdzenie o odwzorowaniu otwartym		29 111
5	Spanish (es) Teorema de la función abierta		20 486
6	Russian (ru) Теорема об открытом отображении		19 000
7	Chinese (zh) 开映射定理		17 042
8	Persian (fa) قضیه نگاشت باز		12 776
9	Hebrew (he) משפט ההעתקה הפתוחה		12 657
10	Italian (it) Teorema della funzione aperta (analisi funzionale)		12 406

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The following table shows the language versions of the article with the highest popularity in the last month.

The most popular language versions of the article "開写像定理 (関数解析)" in June 2025

#	Language	Popularity award	Relative popularity
1	English (en) Open mapping theorem (functional analysis)		2 420
2	French (fr) Théorème de Banach-Schauder		276
3	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		168
4	Japanese (ja) 開写像定理 (関数解析)		123
5	Chinese (zh) 开映射定理		106
6	Spanish (es) Teorema de la función abierta		100
7	Russian (ru) Теорема об открытом отображении		91
8	Polish (pl) Twierdzenie o odwzorowaniu otwartym		88
9	Hebrew (he) משפט ההעתקה הפתוחה		70
10	Italian (it) Teorema della funzione aperta (analisi funzionale)		56

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The following table shows the language versions of the article with the highest Authors’ Interest.

Language versions of the article "開写像定理 (関数解析)" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.

#	Language	AI award	Relative AI
1	English (en) Open mapping theorem (functional analysis)		50
2	French (fr) Théorème de Banach-Schauder		46
3	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		24
4	Hebrew (he) משפט ההעתקה הפתוחה		15
5	Vietnamese (vi) Nguyên lý ánh xạ mở		11
6	Polish (pl) Twierdzenie o odwzorowaniu otwartym		10
7	Russian (ru) Теорема об открытом отображении		10
8	Spanish (es) Teorema de la función abierta		9
9	Ukrainian (uk) Теорема Банаха про обернений оператор		9
10	Persian (fa) قضیه نگاشت باز		8

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The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

Language versions of the article "開写像定理 (関数解析)" with the highest AI in June 2025

#	Language	AI award	Relative AI
1	Persian (fa) قضیه نگاشت باز		1
2	Catalan (ca) Teorema de la funció oberta		0
3	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		0
4	English (en) Open mapping theorem (functional analysis)		0
5	Spanish (es) Teorema de la función abierta		0
6	French (fr) Théorème de Banach-Schauder		0
7	Hebrew (he) משפט ההעתקה הפתוחה		0
8	Italian (it) Teorema della funzione aperta (analisi funzionale)		0
9	Japanese (ja) 開写像定理 (関数解析)		0
10	Dutch (nl) Open afbeeldingsstelling		0

More...

The following table shows the language versions of the article with the highest number of citations.

Language versions of the article "開写像定理 (関数解析)" with the highest Citation Index (CI)

#	Language	CI award	Relative CI
1	English (en) Open mapping theorem (functional analysis)		304
2	Chinese (zh) 开映射定理		90
3	French (fr) Théorème de Banach-Schauder		82
4	Japanese (ja) 開写像定理 (関数解析)		54
5	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		24
6	Spanish (es) Teorema de la función abierta		19
7	Persian (fa) قضیه نگاشت باز		18
8	Polish (pl) Twierdzenie o odwzorowaniu otwartym		14
9	Hebrew (he) משפט ההעתקה הפתוחה		10
10	Italian (it) Teorema della funzione aperta (analisi funzionale)		8

More...

#	Language	Value
ca	Catalan Teorema de la funció oberta
de	German Satz von der offenen Abbildung (Funktionalanalysis)
en	English Open mapping theorem (functional analysis)
es	Spanish Teorema de la función abierta
fa	Persian قضیه نگاشت باز
fr	French Théorème de Banach-Schauder
he	Hebrew משפט ההעתקה הפתוחה
it	Italian Teorema della funzione aperta (analisi funzionale)
ja	Japanese 開写像定理 (関数解析)
nl	Dutch Open afbeeldingsstelling
pl	Polish Twierdzenie o odwzorowaniu otwartym
pt	Portuguese Teorema de Banach-Schauder
ru	Russian Теорема об открытом отображении
sr	Serbian Теорема о отвореном пресликавању
sv	Swedish Satsen om den öppna avbildningen
uk	Ukrainian Теорема Банаха про обернений оператор
vi	Vietnamese Nguyên lý ánh xạ mở
zh	Chinese 开映射定理

Best Rank

Japanese: #441709 07.2022

Global: #348003 11.2021

Best Rank

Japanese: #43528 07.2012

Global: #29362 04.2003

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The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information