File:Topological space examples.svg

From Wikimedia Commons, the free media repository

Jump to: navigation, search

Topological_space_examples.svg(SVG file, nominally 360 × 319 pixels, file size: 12 KB)

Contents

[edit] Summary

Description

Examples and non-examples of topological spaces, based roughly on Figures 12.1 and 12.2 from Munkres' Introduction to Topology. The 6 examples are subsets of the power set of {1,2,3}, with the small circle in the upper left of each denoting the empty set, and in reading order they are:

  • {{}, {1,2,3}} (the trivial topology)
  • {{}, {1}, {1,2,3}}
  • {{}, {1}, {2}, {1,2}, {1,2,3}}
  • {{}, {2}, {1,2}, {2,3}, {1,2,3}}
  • {{}, {2}, {3}, {1,2,3}} (not a topology, because {2} and {3} are in the topology but their union {2,3} is not)
  • {{}, {1,2}, {2,3}, {1,2,3}} (not a topology, because {1,2} and {2,3} are in the topology but their intersection {2} is not)
Date

25 May 2008(2008-05-25)

Source

Own work

Author

Dcoetzee

Permission
(Reusing this image)

See below.

[edit] Licensing

Public domain I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.


Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Azərbaycan | Беларуская (тарашкевіца) | Български | Català | Cebuano | Soranî / کوردی | Česky | Cymraeg | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | Estremeñu | فارسی | Suomi | Français | Galego | עברית | हिन्दी | Hrvatski | Magyar | Հայերեն | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Ripoarisch | Kurdî / كوردی | Latina | Lietuvių | Latviešu | 文言 | Македонски | Bahasa Melayu | Plattdüütsch | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | ไทย | Tagalog | Türkçe | Українська | Vèneto | Tiếng Việt | Walon | 吴语 | 中文 | ‪中文(简体)‬ | ‪中文(繁體)‬ | 粵語 | +/−

Information icon.svg The categories of this image should be checked. Check them now!
  • Remove redundant categories and try to put this image in the most specific category/categories
  • Remove this template

Afrikaans | Alemannisch | Català | Česky | Dansk | Deutsch | Deutsch (Sie-Form) | English | Español | Eesti | Suomi | Français | עברית | Հայերեն | Italiano | 日本語 | Македонски | Malti | Plattdüütsch | Nederlands | Polski | Português | Română | Русский | Slovenčina | ไทย | Vèneto | 中文 | +/−


Usage:

Related galleries:

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current06:54, 26 May 2008Thumbnail for version as of 06:54, 26 May 2008360×319 (12 KB)Dcoetzee (Talk | contribs) ({{Information |Description=Examples and non-examples of topological spaces, based roughly on Figures 12.1 and 12.2 from Munkres' ''Introduction to Topology''. The 6 examples are subsets of the power set of {1,2,3}, with the small circle in the upper left )

The following 2 pages on Wikimedia Commons link to this file. Some pages on other Wikimedia projects may also link to it.

Global file usage

The following other wikis use this file: