https://companal.subwiki.org/w/index.php?action=history&feed=atom&title=Sheaf_of_holomorphic_functions
Sheaf of holomorphic functions - Revision history
2026-07-10T19:06:30Z
Revision history for this page on the wiki
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Vipul: 2 revisions
2008-05-18T19:18:37Z
<p>2 revisions</p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:18, 18 May 2008</td>
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Vipul
https://companal.subwiki.org/w/index.php?title=Sheaf_of_holomorphic_functions&diff=463&oldid=prev
Vipul at 23:36, 18 April 2008
2008-04-18T23:36:36Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:36, 18 April 2008</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===On an open subset in complex numbers===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===On an open subset in complex numbers===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Suppose <math>U \subset \mathbb{C}</math> is an open subset. The '''sheaf of holomorphic functions''' on <math>U</math> is a sheaf of <math>\C</math>-algebras defined as follows:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Suppose <math>U \subset \mathbb{C}</math> is an open subset. The '''sheaf of holomorphic functions''' on <math>U</math> is a sheaf of <math>\<ins style="font-weight: bold; text-decoration: none;">mathbb{</ins>C<ins style="font-weight: bold; text-decoration: none;">}</ins></math>-algebras defined as follows:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* For every open subset <math>V \subset U</math>, the algebra is the <math>\mathbb{C}</math>-algebra of holomorphic functions on <math>V</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* For every open subset <math>V \subset U</math>, the algebra is the <math>\mathbb{C}</math>-algebra of holomorphic functions on <math>V</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* The restriction maps are simply function restriction</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* The restriction maps are simply function restriction</div></td></tr>
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Vipul
https://companal.subwiki.org/w/index.php?title=Sheaf_of_holomorphic_functions&diff=462&oldid=prev
Vipul: New page: ==Definition== ===On an open subset in complex numbers=== Suppose <math>U \subset \mathbb{C}</math> is an open subset. The '''sheaf of holomorphic functions''' on <math>U</math> is a she...
2008-04-18T23:35:51Z
<p>New page: ==Definition== ===On an open subset in complex numbers=== Suppose <math>U \subset \mathbb{C}</math> is an open subset. The '''sheaf of holomorphic functions''' on <math>U</math> is a she...</p>
<p><b>New page</b></p><div>==Definition==<br />
<br />
===On an open subset in complex numbers===<br />
<br />
Suppose <math>U \subset \mathbb{C}</math> is an open subset. The '''sheaf of holomorphic functions''' on <math>U</math> is a sheaf of <math>\C</math>-algebras defined as follows:<br />
<br />
* For every open subset <math>V \subset U</math>, the algebra is the <math>\mathbb{C}</math>-algebra of holomorphic functions on <math>V</math><br />
* The restriction maps are simply function restriction</div>
Vipul