Čech cohomology
cohomology theory based on the intersection properties of open covers of a topological space
| rdfs:label |
"Čech cohomology"@en
|
|
skos:alt |
"Aleksandrov–Čech cohomology"@en
"spectral cohomology"@en
|
| schema:description |
"cohomology theory based on the intersection properties of open covers of a topological space"@en
|
|
schema:date |
"2026-10-01T05:54:48+00:00"^^xsd:dateTime |
| schema:version | 2551643446 |
| wikibase:identifiers | 5 |
| wikibase:sitelinks | 12 |
| wikibase:statements | 23 |
| p:P10283 | wd:statement/Q1095535-0B26C914-CBBF-40C0-9119-7ACE5C2BBBC7 |
| p:P138 | wd:statement/Q1095535-214c4661-4ccd-e1be-2bfe-993f1f2c9711 |
| wd:statement/Q1095535-545c5a3a-4d35-5d89-90a2-c7f5fef5744d | |
| p:P18 | wd:statement/Q1095535-17d7e1ad-46e1-bf24-1f50-806bd1c1e149 |
| p:P2534 | wd:statement/Q1095535-acafc969-4be4-ea54-4557-bf8fb395aebc |
| p:P2579 | wd:statement/Q1095535-41FBE643-F376-4E31-935B-092566353857 |
| p:P279 | wd:statement/Q1095535-7157bd14-4d5c-3318-bf20-edceb7187dbc |
| p:P31 | wd:statement/Q1095535-23ff590b-435b-50f8-97ab-090bae394656 |
| wd:statement/Q1095535-bf562ab3-40ae-8ca7-75cc-d252e0248874 | |
| wd:statement/Q1095535-e823981a-472d-458b-335f-d4ad59c73ce5 | |
| p:P361 | wd:statement/Q1095535-7D992BFA-06B0-475B-883D-A575D8D3CFE8 |
| wd:statement/Q1095535-F3FCA67B-2A27-40D9-BA83-65571BEC8D73 | |
| p:P4215 | wd:statement/Q1095535-93CF608D-6E1D-4C80-B7B1-D5C6C68B51BE |
| p:P575 | wd:statement/Q1095535-4bc70da2-40b1-2fda-4e43-1df83a3054f2 |
| p:P61 | wd:statement/Q1095535-cb96322d-4d48-cf36-7d27-6895a0141de9 |
| p:P6104 | wd:statement/Q1095535-6A80247A-C9D4-4E39-8CEF-C35DFCA4DE63 |
| p:P6366 | wd:statement/Q1095535-F51C108F-684A-43BB-BA52-81FFE17EBCE1 |
| p:P646 | wd:statement/Q1095535-4CC9E2E2-DC1C-4E97-B6F2-8EE0E140F907 |
| p:P7235 | wd:statement/Q1095535-3c5dd9c7-4654-2e6d-ba13-5ac39dda411d |
| wd:statement/Q1095535-6f981121-43ca-6075-b2c8-9601d807e6e2 | |
| wd:statement/Q1095535-b8a83585-435f-c222-6f03-d6319e28ebd5 | |
| p:P7554 | wd:statement/Q1095535-5c4d54c3-49a3-8d5a-fbc8-bd72fd4fbaf0 |
| p:P910 | wd:statement/Q1095535-39bbe755-4992-129b-0430-d89a8c294b28 |
|
p:direct- |
<https:/ |
| wdt:P10283 | "C74196217" |
| wdt:P138 | Pavel Aleksandrov |
| Eduard Čech | |
| wdt:P18 |
<http:/ |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><msub><mi>δ</mi><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></msub><mo stretchy="false">:</mo><msup><mi>C</mi><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></msup><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒰</mi></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">ℱ</mi></mrow><mo stretchy="false">)</mo></mtd><mtd><mo stretchy="false" accent="false">→</mo><msup><mi>C</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>q</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow></msup><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒰</mi></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">ℱ</mi></mrow><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>f</mi></mtd><mtd><mo stretchy="false">↦</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>σ</mi><mo stretchy="false">↦</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>j</mi><mo stretchy="false">=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>q</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow></munderover></mstyle><mo stretchy="false">(</mo><mo stretchy="false">−</mo><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msup><msubsup><mi data-mjx-texclass="OP" mathvariant="normal">res</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><mi>σ</mi><mo stretchy="false">|</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mi>σ</mi><mo stretchy="false">|</mo></mrow></mrow></msubsup><mi>f</mi><mo stretchy="false">(</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mi>σ</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | homological algebra |
| wdt:P279 | topological property |
| wdt:P31 | cohomology |
| mathematical theory | |
| mathematical concept | |
| wdt:P361 | theory of open covers of topological spaces |
| sheaf cohomology | |
| wdt:P4215 | "Čech cohomology" |
| wdt:P575 | "1927-01-01T00:00:00+00:00"^^xsd:dateTime |
| wdt:P61 | Pavel Aleksandrov |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "74196217" |
| wdt:P646 | "/m/03hpyc" |
| wdt:P7235 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">ℱ</mi></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒰</mi></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>δ</mi><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></msub></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P7554 | "Čech_cohomology" |
| wdt:P910 | wd:Q114728443 |
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