#+TITLE: Searx API request This is related to issue https://gitlab.iscpif.fr/gargantext/haskell-gargantext/issues/70 #+begin_src restclient :domain := "https://searx.frame.gargantext.org" POST :domain/ Content-Type: application/x-www-form-urlencoded category_general=1&q=banach%20space&pageno=1&time_range=None&language=en-US&format=json #+end_src #+RESULTS: #+BEGIN_SRC js { "query": "banach space", "number_of_results": 93700.0, "results": [ { "url": "https://en.wikipedia.org/wiki/Banach_space", "title": "Banach space", "engine": "wikipedia", "parsed_url": [ "https", "en.wikipedia.org", "/wiki/Banach_space", "", "", "" ], "engines": [ "wikipedia" ], "positions": [ 1 ], "score": 1.0, "category": "general", "pretty_url": "https://en.wikipedia.org/wiki/Banach_space" }, { "url": "http://mathworld.wolfram.com/BanachSpace.html", "title": "Banach Space -- from Wolfram MathWorld", "content": "10/05/2021 · A Banach space is a complete vector space with a norm . Two norms and are called equivalent if they give the same topology , which is equivalent to the existence of constants and such that. (1) and. (2) hold for all . In the finite-dimensional case, all norms are equivalent.", "engine": "bing", "parsed_url": [ "http", "mathworld.wolfram.com", "/BanachSpace.html", "", "", "" ], "engines": [ "bing" ], "positions": [ 1 ], "score": 1.0, "category": "general", "pretty_url": "http://mathworld.wolfram.com/BanachSpace.html" }, { "url": "https://en.wikipedia.org/wiki/List_of_Banach_spaces", "title": "List of Banach spaces - Wikipedia", "content": "25 lignes · Classical Banach spaces. According to Diestel (1984, Chapter VII), the classical Banach …", "engine": "bing", "parsed_url": [ "https", "en.wikipedia.org", "/wiki/List_of_Banach_spaces", "", "", "" ], "engines": [ "bing" ], "positions": [ 2 ], "score": 0.5, "category": "general", "pretty_url": "https://en.wikipedia.org/wiki/List_of_Banach_spaces" }, { "url": "https://encyclopediaofmath.org/wiki/Banach_space", "title": "Banach space - Encyclopedia of Mathematics", "content": "According to Diestel (1984, Chapter VII), the classical Banach spaces are those defined by Dunford & Schwartz (1958), which is the source for the following table. Here K denotes the field of real numbers or complex numbers and I is a closed and bounded interval [a,b]. The number p is a real number with 1 < p < ∞, and q is its Hölder conjugate (also with 1 < q < ∞), so that the next equation holds: $${\\displaystyle {\\frac {1}{q}}+{\\frac {1}{p}}=1,}$$According to Diestel (1984, Chapter VII), the classical Banach spaces are those defined by Dunford & Schwartz (1958), which is the source for the following table. Here K denotes the field of real numbers or complex numbers and I is a closed and bounded interval [a,b]. The number p is a real number with 1 < p < ∞, and q is its Hölder conjugate (also with 1 < q < ∞), so that the next equation holds: $${\\displaystyle {\\frac {1}{q}}+{\\frac {1}{p}}=1,}$$and thus $${\\displaystyle q={\\frac {p}{p-1}}.}$$The symbol Σ denotes a σ-algebra of sets, and Ξ denotes just an algebra of sets (for spaces only requiring finite additivity, such as the ba space). The symbol μ denotes a positive measure: that is, a real-valued positive set function defined on a σ-algebra which is countably additive.", "engine": "bing", "parsed_url": [ "https", "encyclopediaofmath.org", "/wiki/Banach_space", "", "", "" ], "engines": [ "bing" ], "positions": [ 3 ], "score": 0.3333333333333333, "category": "general", "pretty_url": "https://encyclopediaofmath.org/wiki/Banach_space" }, { "url": "https://www.techopedia.com/definition/17852/banach-space", "title": "What is Banach Space? - Definition from Techopedia", "content": "22/03/2017 · In functional analysis, a Banach space is a normed vector space that allows vector length to be computed. When the vector space is normed, that means that each vector other than the zero vector has a length that is greater than zero. The length and distance between two vectors can thus be computed. The vector space is complete, meaning a Cauchy sequence of vectors in a Banach space …", "engine": "bing", "parsed_url": [ "https", "www.techopedia.com", "/definition/17852/banach-space", "", "", "" ], "engines": [ "bing" ], "positions": [ 4 ], "score": 0.25, "category": "general", "pretty_url": "https://www.techopedia.com/definition/17852/banach-space" }, { "url": "https://www.sciencedirect.com/topics/mathematics/banach-spaces", "title": "Banach Spaces - an overview | ScienceDirect Topics", "content": "A Banach spaceis a complete normed linear space. Example 4.3 The spaces RN,CNare vector spaces which are also complete metric spaces with any of the norms ∥⋅∥p, hence they are Banach spaces. Similarly C(E), Lp(E) are Banach spaces with norms indicated above. □", "engine": "bing", "parsed_url": [ "https", "www.sciencedirect.com", "/topics/mathematics/banach-spaces", "", "", "" ], "engines": [ "bing" ], "positions": [ 5 ], "score": 0.2, "category": "general", "pretty_url": "https://www.sciencedirect.com/topics/mathematics/banach-spaces" }, { "url": "https://people.math.gatech.edu/~heil/handouts/banach.pdf", "title": "Banach Spaces - gatech.edu", "content": "07/09/2006 · have already said that “a Banach space is complete” if every Cauchy sequence in the space converges. The term “complete sequences” defined in this section is a completely separate definition that applies to sets of vectors in a Hilbert or Banach space (although we …", "engine": "bing", "parsed_url": [ "https", "people.math.gatech.edu", "/~heil/handouts/banach.pdf", "", "", "" ], "engines": [ "bing" ], "positions": [ 6 ], "score": 0.16666666666666666, "category": "general", "pretty_url": "https://people.math.gatech.edu/~heil/handouts/banach.pdf" }, { "url": "https://ncatlab.org/nlab/show/Banach+space", "title": "Banach space in nLab", "content": "", "engine": "bing", "parsed_url": [ "https", "ncatlab.org", "/nlab/show/Banach+space", "", "", "" ], "engines": [ "bing" ], "positions": [ 7 ], "score": 0.14285714285714285, "category": "general", "pretty_url": "https://ncatlab.org/nlab/show/Banach+space" }, { "url": "https://www.numerade.com/books/chapter/structure-of-banach-spaces/", "title": "Structure of Banach Spaces | Functional Analysis", "content": "Structure of Banach Spaces, Functional Analysis and InfiniteDimensional Geometry - Marián Fabian, Petr Habala, Petr Hájek | All the textbook answers and step-b…", "engine": "bing", "parsed_url": [ "https", "www.numerade.com", "/books/chapter/structure-of-banach-spaces/", "", "", "" ], "engines": [ "bing" ], "positions": [ 8 ], "score": 0.125, "category": "general", "pretty_url": "https://www.numerade.com/books/chapter/structure-of-banach-spaces/" }, { "url": "http://www.ma.huji.ac.il/~razk/iWeb/My_Site/Teaching_files/Banach.pdf", "title": "2. Banach spaces - ma.huji.ac.il", "content": "Definition 2.1A Banach space is a complete, normed, vector space. Comment 2.1Completeness is a metric space concept. In a normed space the metric is d(x,y)=x−y. Note that this metric satisfies the following “special\" properties: ¿ The underlying space is a vector space.", "engine": "bing", "parsed_url": [ "http", "www.ma.huji.ac.il", "/~razk/iWeb/My_Site/Teaching_files/Banach.pdf", "", "", "" ], "engines": [ "bing" ], "positions": [ 9 ], "score": 0.1111111111111111, "category": "general", "pretty_url": "http://www.ma.huji.ac.il/~razk/iWeb/My_Site/Teaching_files/Banach.pdf" } ], "answers": [], "corrections": [], "infoboxes": [ { "infobox": "Banach space", "id": "https://en.wikipedia.org/wiki/Banach_space", "content": "In mathematics, more specifically in functional analysis, a Banach space (pronounced [ˈbanax]) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well defined limit that is within the space.", "img_src": null, "urls": [ { "title": "Wikipedia", "url": "https://en.wikipedia.org/wiki/Banach_space" }, { "title": "Wikidata", "url": "https://www.wikidata.org/wiki/Q194397?uselang=en" } ], "engine": "wikidata", "attributes": [ { "label": "Inception", "value": "1920" } ] } ], "suggestions": [], "unresponsive_engines": [] } // POST https://searx.frame.gargantext.org/ // HTTP/1.1 200 OK // Server: nginx/1.14.2 // Date: Tue, 27 Jul 2021 17:20:48 GMT // Content-Type: application/json // Content-Length: 8020 // Connection: keep-alive // Server-Timing: total;dur=1826.455, total_0_go;dur=248.527, total_1_wp;dur=352.718, total_2_bi;dur=628.671, total_3_wd;dur=1822.518, load_0_go;dur=234.185, load_1_wp;dur=348.323, load_2_bi;dur=595.242, load_3_wd;dur=1778.783 // Request duration: 2.159931s #+END_SRC