File:Filter vs ultrafilter.svg
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Original file (SVG file, nominally 528 × 415 pixels, file size: 18 KB)
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Summary
| Description |
English: The Hasse diagram shows the set of all subsets of {1,2,3,4}, partially ordered by set inclusion (⊆). The upper set ↑{1,4} is highlighted in dark green, it is a filter. However, it is not an ultrafilter, since it can still be extended to the properly larger filter ↑{1}, shown in light green. The latter cannot be extended to any nontrivial larger filter in turn, it is hence an ultrafilter. |
| Date | |
| Source | Own work based on: Upset.svg |
| Author | Jochen Burghardt |
| Other versions |
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| SVG development |  This diagram was created with Inkscape.  This diagram uses embedded text that can be easily translated using a text editor. |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:06, 26 February 2020 | | 528 × 415 (18 KB) | wikimediacommons>Jochen Burghardt | change colors towards more definite names ("light green", "dark green") |
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