File:Schroder-Bernstein counterexample.jpg
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| Description | Counterexample to the Schröder-Bernstein theorem for images rather than plain sets. The right image can be embedded into the left one (see File:Schroder-Bernstein counterexample R in L.jpg), and vice versa (see File:Schroder-Bernstein counterexample L in R.jpg). However, both images aren't similar. This demonstrates that images don't have the Schröder-Bernstein property. — File:Schroder-Bernstein counterexample noncontiuous bijection.jpg shows the bijection between the plain (unstructured) pixel sets obtained by the Schröder-Bernstein theorem; it is noncontinuous. — See File:Schroder-Bernstein counterexample - Making of.jpg for the making of the left image with two mirrors. Many fractals can be used to generate similar counterexamples. |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
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| current | 19:59, 2 February 2015 | | 6,800 × 4,400 (1.34 MB) | Jochen Burghardt (talk | contribs) | {{Information |Description=Counterexample to the Schrouml;der-Bernstein theorem for images rather thn plain sets. |Source={{own}} |Date=2015-02-02 |Author=Jochen Burghardt |Permission= |other_versions= }} |
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