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...type space|stereotype]] and are in the stereotype duality relations with [[Fréchet space]]s:{{sfn|Akbarov|2003|p=220}}{{sfn|Akbarov|2009|p=466}} :* for any Fréchet space <math>X</math> its stereotype dual space<ref>The ''stereotype dual'' ...

* The category of [[Fréchet space]]s is quasi-abelian. ...ef>{{cite journal |last1=Beilinson |first1=A |title=Remarks on topological algebras |journal=Moscow Mathematical Journal |date=2008 |volume=8 |issue=1}}</ref> ...

...of a vector space is the field of real numbers or that of complex numbers. Algebras are not assumed to be unital. {{defn|1=The [[Anderson–Kadec theorem]] says a separable infinite-dimensional Fréchet space is isomorphic to <math>\mathbb{R}^{\mathbb{N}}</math>.}} ...

With this topology, <math>C^k(U)</math> becomes a locally convex [[Fréchet space]] that is {{em|not}} [[Normable space|normable]]. Every element of <m ...<math>C^\infty(U)</math> can be obtained by taking a suitable countable [[Fréchet combination]] of any one of the above defining families of seminorms (''A'' ...

...p>[0,1]}} is represented by integration is jointly attributed to {{harvtxt|Fréchet|1907}} and {{harvtxt|Riesz|1907}}. The general result, that the dual of a H ...underlies much of the existing Hilbert space theory was generalized to C*-algebras.<ref>{{harvnb|Murphy|1990|p=72}}</ref> These techniques are now basic in ab ...

...sense to denote reflexive and symmetric relations defined on universes of algebras that are also compatible with operations of a given algebra, ''i.e.'', they ...roup=2|The basic facts about closure of a set were first pointed out by M. Fréchet in{{cref2|11|1}}, and elaborated by B. Knaster and C. Kuratowski in{{cref2| ...

...se in <math>\operatorname{Val}(V)</math>; it comes equipped with a natural Fréchet-space topology, which is finer than the one induced from <math>\operatornam The pullback is a morphism of filtered algebras. ...

<li><math>U</math> does {{em|not}} contain the [[Fréchet filter]] on <math>X</math> as a subset.</li> <li>[[Stone's representation theorem for Boolean algebras]].</li> ...

...=Information Processing in Medical Imaging |chapter=Finite-Dimensional Lie Algebras for Fast Diffeomorphic Image Registration |date=2015 |volume=24|pages=249–2 ...variation of the vector field. The directional derivative calculates the [[Fréchet derivative#Relation to the Gateaux derivative|Gateaux derivative]] as calcu ...