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 August 1, 2024). 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 229 registered Wikipedia users in all languages.

The article is cited 52 times in Japanese Wikipedia and cited 660 times in all languages.

The highest Authors Interest rank from 2001:

• Local (Japanese): #43530 in July 2012
• Global: #29369 in April 2003

The highest popularity rank from 2008:

• Local (Japanese): #442088 in July 2022
• Global: #363164 in November 2023

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 August 1, 2024 (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)		38.4556
2	French (fr) Théorème de Banach-Schauder		35.3134
3	Dutch (nl) Open afbeeldingsstelling		24.1896
4	Portuguese (pt) Teorema de Banach-Schauder		19.7935
5	Catalan (ca) Teorema de la funció oberta		16.5507
6	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		12.4388
7	Chinese (zh) 开映射定理		9.6097
8	Italian (it) Teorema della funzione aperta (analisi funzionale)		8.3287
9	Hebrew (he) משפט ההעתקה הפתוחה		5.1715
10	Swedish (sv) Satsen om den öppna avbildningen		4.9446

More...

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)		336 885
2	French (fr) Théorème de Banach-Schauder		78 403
3	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		50 750
4	Polish (pl) Twierdzenie o odwzorowaniu otwartym		28 446
5	Spanish (es) Teorema de la función abierta		19 404
6	Russian (ru) Теорема об открытом отображении		18 090
7	Chinese (zh) 开映射定理		15 823
8	Persian (fa) قضیه نگاشت باز		12 547
9	Hebrew (he) משפט ההעתקה הפתוחה		11 721
10	Italian (it) Teorema della funzione aperta (analisi funzionale)		11 662

More...

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 July 2024

#	Language	Popularity award	Relative popularity
1	English (en) Open mapping theorem (functional analysis)		2 468
2	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		243
3	French (fr) Théorème de Banach-Schauder		192
4	Japanese (ja) 開写像定理 (関数解析)		182
5	Hebrew (he) משפט ההעתקה הפתוחה		102
6	Italian (it) Teorema della funzione aperta (analisi funzionale)		90
7	Chinese (zh) 开映射定理		80
8	Spanish (es) Teorema de la función abierta		67
9	Russian (ru) Теорема об открытом отображении		43
10	Vietnamese (vi) Nguyên lý ánh xạ mở		34

More...

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)		47
2	French (fr) Théorème de Banach-Schauder		42
3	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		24
4	Hebrew (he) משפט ההעתקה הפתוחה		15
5	Polish (pl) Twierdzenie o odwzorowaniu otwartym		10
6	Russian (ru) Теорема об открытом отображении		10
7	Vietnamese (vi) Nguyên lý ánh xạ mở		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

More...

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 July 2024

#	Language	AI award	Relative AI
1	English (en) Open mapping theorem (functional analysis)		4
2	Italian (it) Teorema della funzione aperta (analisi funzionale)		1
3	Catalan (ca) Teorema de la funció oberta		0
4	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		0
5	Spanish (es) Teorema de la función abierta		0
6	Persian (fa) قضیه نگاشت باز		0
7	French (fr) Théorème de Banach-Schauder		0
8	Hebrew (he) משפט ההעתקה הפתוחה		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)		301
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)		52
5	German (de) Satz von der offenen Abbildung (Funktionalanalysis)		23
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		9
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: #442088 07.2022

Global: #363164 11.2023

Best Rank

Japanese: #43530 07.2012

Global: #29369 04.2003

On 26 June 2025 in multilingual Wikipedia, Internet users most often read articles on the following topics: 2025 FIFA Club World Cup, Jeff Bezos, Zohran Mamdani, Lauren Sánchez, Northrop B-2 Spirit, 2025 NBA draft, F1, FIFA Club World Cup, 28 Years Later, Ali Khamenei.

In Japanese Wikipedia the most popular articles on that day were: 宮島三郎, 椎名林檎, 福田典子, TOKIO, ジャイアント・ホグウィード, 引田天功 (2代目), 蒼井優, 光宗薫, 国分太一, 長瀬智也.

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 August, 2024. When calculating current popularity and AI of articles data from July 2024 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2023... More information