Open mapping theorem (complex analysis)

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Open mapping theorem (complex analysis)

Quality:

Open mapping theorem - Theorem that holomorphic functions on complex domains are open maps. Article "Open mapping theorem (complex analysis)" in English Wikipedia has 10.3 points for quality (as of July 1, 2025). The article contains 0 references and 4 sections.

This article has the best quality in French Wikipedia. However, this article is the most popular in English version.

Since the creation of article "Open mapping theorem (complex analysis)", its content was written by 26 registered users of English Wikipedia and edited by 96 registered Wikipedia users in all languages.

The article is cited 8 times in English Wikipedia and cited 42 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #147386 in August 2012
  • Global: #150947 in November 2018

The highest popularity rank from 2008:

  • Local (English): #512563 in July 2021
  • Global: #750942 in July 2021

There are 10 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.

Languages with the highest quality

#LanguageQuality gradeQuality score
1French (fr)
Théorème de l'image ouverte
17.5442
2Russian (ru)
Принцип сохранения области
10.5761
3English (en)
Open mapping theorem (complex analysis)
10.3417
4Turkish (tr)
Açık gönderim teoremi (karmaşık analiz)
7.2321
5Italian (it)
Teorema della funzione aperta (analisi complessa)
6.5685
6Ukrainian (uk)
Принцип збереження області
6.1762
7Japanese (ja)
開写像定理 (複素解析)
4.5273
8Chinese (zh)
开映射定理 (复分析)
3.6908
9German (de)
Offenheitsprinzip
2.451
10Swedish (sv)
Satsen om den öppna avbildningen (komplex analys)
0.1436
More...

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

Most popular in all the time

The most popular language versions of the article "Open mapping theorem (complex analysis)" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Open mapping theorem (complex analysis)
181 315
2German (de)
Offenheitsprinzip
28 018
3French (fr)
Théorème de l'image ouverte
21 550
4Russian (ru)
Принцип сохранения области
9 514
5Japanese (ja)
開写像定理 (複素解析)
6 006
6Italian (it)
Teorema della funzione aperta (analisi complessa)
5 928
7Turkish (tr)
Açık gönderim teoremi (karmaşık analiz)
4 078
8Chinese (zh)
开映射定理 (复分析)
2 041
9Ukrainian (uk)
Принцип збереження області
345
10Swedish (sv)
Satsen om den öppna avbildningen (komplex analys)
106
More...

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

Most popular in June 2025

The most popular language versions of the article "Open mapping theorem (complex analysis)" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Open mapping theorem (complex analysis)
1 044
2German (de)
Offenheitsprinzip
103
3Japanese (ja)
開写像定理 (複素解析)
86
4French (fr)
Théorème de l'image ouverte
43
5Russian (ru)
Принцип сохранения области
35
6Chinese (zh)
开映射定理 (复分析)
32
7Turkish (tr)
Açık gönderim teoremi (karmaşık analiz)
26
8Italian (it)
Teorema della funzione aperta (analisi complessa)
24
9Swedish (sv)
Satsen om den öppna avbildningen (komplex analys)
4
10Ukrainian (uk)
Принцип збереження області
3
More...

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

The highest AI

Language versions of the article "Open mapping theorem (complex analysis)" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1German (de)
Offenheitsprinzip
26
2English (en)
Open mapping theorem (complex analysis)
26
3Russian (ru)
Принцип сохранения области
11
4Italian (it)
Teorema della funzione aperta (analisi complessa)
7
5Turkish (tr)
Açık gönderim teoremi (karmaşık analiz)
7
6French (fr)
Théorème de l'image ouverte
6
7Chinese (zh)
开映射定理 (复分析)
6
8Ukrainian (uk)
Принцип збереження області
3
9Japanese (ja)
開写像定理 (複素解析)
2
10Swedish (sv)
Satsen om den öppna avbildningen (komplex analys)
2
More...

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

The highest AI in June 2025

Language versions of the article "Open mapping theorem (complex analysis)" with the highest AI in June 2025
#LanguageAI awardRelative AI
1German (de)
Offenheitsprinzip
0
2English (en)
Open mapping theorem (complex analysis)
0
3French (fr)
Théorème de l'image ouverte
0
4Italian (it)
Teorema della funzione aperta (analisi complessa)
0
5Japanese (ja)
開写像定理 (複素解析)
0
6Russian (ru)
Принцип сохранения области
0
7Swedish (sv)
Satsen om den öppna avbildningen (komplex analys)
0
8Turkish (tr)
Açık gönderim teoremi (karmaşık analiz)
0
9Ukrainian (uk)
Принцип збереження області
0
10Chinese (zh)
开映射定理 (复分析)
0
More...

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

The highest CI

Language versions of the article "Open mapping theorem (complex analysis)" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1German (de)
Offenheitsprinzip
11
2English (en)
Open mapping theorem (complex analysis)
8
3French (fr)
Théorème de l'image ouverte
7
4Italian (it)
Teorema della funzione aperta (analisi complessa)
3
5Turkish (tr)
Açık gönderim teoremi (karmaşık analiz)
3
6Ukrainian (uk)
Принцип збереження області
3
7Chinese (zh)
开映射定理 (复分析)
3
8Japanese (ja)
開写像定理 (複素解析)
2
9Russian (ru)
Принцип сохранения области
2
10Swedish (sv)
Satsen om den öppna avbildningen (komplex analys)
0
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2025:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2025:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
deGerman
Offenheitsprinzip
enEnglish
Open mapping theorem (complex analysis)
frFrench
Théorème de l'image ouverte
itItalian
Teorema della funzione aperta (analisi complessa)
jaJapanese
開写像定理 (複素解析)
ruRussian
Принцип сохранения области
svSwedish
Satsen om den öppna avbildningen (komplex analys)
trTurkish
Açık gönderim teoremi (karmaşık analiz)
ukUkrainian
Принцип збереження області
zhChinese
开映射定理 (复分析)

Popularity rank trends

Best Rank English:
#512563
07.2021
Global:
#750942
07.2021

AI rank trends

Best Rank English:
#147386
08.2012
Global:
#150947
11.2018

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Open mapping theorem from Wikipedia articles about Open mapping theorem, Maximum modulus principle, Rouchés theorem, Open mapping theorem and Complex analysis. Whereas reading the article about Open mapping theorem people most often go to Wikipedia articles on Rouchés theorem, Maximum modulus principle, Identity theorem, Invariance of domain and Schwarz lemma.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

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About WikiRank

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