Fréchet space
locally convex space that is complete with respect to a translation-invariant metric
| rdfs:label |
"Fréchet space"@en
|
|
skos:alt |
"Frechet space"@en
|
| schema:description |
"locally convex space that is complete with respect to a translation-invariant metric"@en
|
|
schema:date |
"2026-09-06T21:06:19+00:00"^^xsd:dateTime |
| schema:version | 2541315821 |
| wikibase:identifiers | 11 |
| wikibase:sitelinks | 14 |
| wikibase:statements | 23 |
| p:P10283 | wd:statement/Q1471397-FADEF28E-4D02-4A4A-8EC0-CBB00E4EC1E5 |
| p:P138 | wd:statement/q1471397-D2976613-9C2C-4818-AC44-1D6DF3179358 |
| p:P1889 | wd:statement/Q1471397-F8005587-CEE1-44F7-973E-C1DF8E2377BA |
| wd:statement/Q1471397-af7ee7b8-4580-3a88-09ef-b0494ff35adb | |
| p:P2534 | wd:statement/Q1471397-d39d9540-4a4f-45be-8b63-ea119b9820b7 |
| p:P2581 | wd:statement/Q1471397-F8687ABE-1297-43BC-A386-4F1F3AEABAAA |
| p:P279 | wd:statement/Q1471397-0d75a333-4b57-d936-4306-a0fe07d9f00b |
| wd:statement/Q1471397-1758897f-40fe-8f7f-7cea-8ff6e85b5a5d | |
| wd:statement/Q1471397-753cb208-4095-3291-dbe8-4ccca9a45f6c | |
| wd:statement/Q1471397-b062022f-4e38-973f-4542-5dc56f24bd0c | |
| wd:statement/Q1471397-b422dac0-4fd3-4e5d-832c-fb6f87254c9e | |
| wd:statement/Q1471397-d5b93191-4a58-196f-479a-01a67b39c4a6 | |
| p:P2812 | wd:statement/Q1471397-92511450-4bb0-9fa8-5fb2-06c20966926f |
| p:P31 | wd:statement/Q1471397-75481abc-46c8-eca6-94d9-7e6257ce6842 |
| p:P3827 | wd:statement/Q1471397-550CB405-41C7-4158-B8E1-68BEE8AF8AD0 |
| p:P4215 | wd:statement/Q1471397-A778617F-8A21-4A29-B7F8-63866F262775 |
| p:P6104 | wd:statement/Q1471397-2D56A9BA-13E1-427E-80F5-47D365D94A78 |
| p:P6366 | wd:statement/Q1471397-BAADB9D1-420B-4BD4-A64C-38DD44FA98A2 |
| p:P646 | wd:statement/Q1471397-114F4F77-535F-4116-8655-4958362B6125 |
| p:P7305 | wd:statement/Q1471397-7136AA7D-F89E-4F94-A68A-5ADF0B67F1D2 |
| p:P7554 | wd:statement/Q1471397-f109eb7b-440c-df92-a162-f4fbbd8aa484 |
| p:P7726 | wd:statement/Q1471397-18d3eec3-489b-0117-99e9-9b3aaf60fe82 |
| p:P9621 | wd:statement/Q1471397-d1c3c952-4ce0-cec5-7f24-997be91b3599 |
|
p:direct- |
<http:/ |
|
p:direct- |
<https:/ |
| wdt:P10283 | "C117145882" |
| wdt:P138 | Maurice René Fréchet |
| wdt:P1889 | sequential space |
| T1 space | |
| 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></mtd><mtd><mo stretchy="false">‖</mo><mo stretchy="false">−</mo><msub><mo stretchy="false">‖</mo><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo stretchy="false">‖</mo><mo stretchy="false">−</mo><msub><mo stretchy="false">‖</mo><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo stretchy="false">:</mo><mi>X</mi><mo stretchy="false" accent="false">→</mo><msub><mrow data-mjx-texclass="ORD"><mi>ℝ</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">≥</mo><mn>0</mn></mrow></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">‖</mo><mi>λ</mi><mi>x</mi><msub><mo stretchy="false">‖</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">=</mo><mo stretchy="false">|</mo><mi>λ</mi><mo stretchy="false">|</mo><mo stretchy="false">‖</mo><mi>x</mi><msub><mo stretchy="false">‖</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mo stretchy="false">‖</mo><mi>x</mi><mo stretchy="false">+</mo><mi>y</mi><msub><mo stretchy="false">‖</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">≤</mo><mo stretchy="false">‖</mo><mi>x</mi><msub><mo stretchy="false">‖</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">+</mo><mo stretchy="false">‖</mo><mi>y</mi><msub><mo stretchy="false">‖</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mi>x</mi><mo stretchy="false">=</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟺</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">∀</mi><mi>k</mi><mo>></mo><mn>0</mn><mo stretchy="false">:</mo><mo stretchy="false">‖</mo><mi>x</mi><msub><mo stretchy="false">‖</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mi>U</mi><mo stretchy="false">∈</mo><mi data-mjx-texclass="OP" mathvariant="normal">Open</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟺</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">∀</mi><mi>u</mi><mo stretchy="false">∈</mo><mi>U</mi><mi mathvariant="normal">∃</mi><mi>K</mi><mo>></mo><mn>0</mn><mo>,</mo><mi>r</mi><mo>></mo><mn>0</mn><mo stretchy="false">:</mo><mo fence="false" stretchy="false">{</mo><mi>x</mi><mo stretchy="false">∈</mo><mi>X</mi><mo stretchy="false">:</mo><mi mathvariant="normal">∀</mi><mi>k</mi><mo stretchy="false">≥</mo><mi>K</mi><mo stretchy="false">:</mo><mo stretchy="false">‖</mo><mi>u</mi><mo stretchy="false">−</mo><mi>x</mi><msub><mo stretchy="false">‖</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo><</mo><mi>r</mi><mo fence="false" stretchy="false">}</mo><mo stretchy="false">⊂</mo><mi>U</mi></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2581 | "01649117n" |
| wdt:P279 | Baire space |
| webbed space | |
| LF-space | |
| F-space | |
| Fréchet manifold | |
| stereotype space | |
| wdt:P2812 | "FrechetSpace" |
| wdt:P31 | mathematical concept |
| wdt:P3827 | "frechet-topologies" |
| wdt:P4215 | "Fréchet space" |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "117145882" |
| wdt:P646 | "/m/01hzvp" |
| wdt:P7305 | "3902656" |
| wdt:P7554 | "Fréchet_space" |
| wdt:P7726 | "FrechetSpace" |
| wdt:P9621 | "spazio-di-frechet" |
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