docs/search-api.org

   1 #+TITLE: Searx API request
   2
   3 This is related to issue
   4 https://gitlab.iscpif.fr/gargantext/haskell-gargantext/issues/70
   5
   6 #+begin_src restclient
   7   :domain := "https://searx.frame.gargantext.org"
   8   POST :domain/
   9   Content-Type: application/x-www-form-urlencoded
  10   category_general=1&q=banach%20space&pageno=1&time_range=None&language=en-US&format=json
  11 #+end_src
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  13 #+RESULTS:
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  43       "title": "Banach Space -- from Wolfram MathWorld",
  44       "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.",
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  67       "content": "25 lignes · Classical Banach spaces. According to Diestel (1984, Chapter VII), the classical Banach …",
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  90       "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.",
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 113       "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 …",
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 136       "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. □",
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 159       "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 …",
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 228       "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.",
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 255       "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.",
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