In mathematics, a Grothendieck space, named after Alexander Grothendieck, is a Banach space in which every sequence in its continuous dual space that converges in the weak-* topology (also known as the topology of pointwise convergence) will also converge when is endowed with which is the weak topology induced on by its bidual. Said differently, a Grothendieck space is a Banach space for which a sequence in its dual space converges weak-* if and only if it converges weakly.
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a Grothendieckspace, named after Alexander Grothendieck, is a Banach space X {\displaystyle X} in which every sequence in its continuous dual space X...
Alexander Grothendieck (/ˈɡroʊtəndiːk/; German pronunciation: [ˌalɛˈksandɐ ˈɡʁoːtn̩ˌdiːk] ; French: [ɡʁɔtɛndik]; 28 March 1928 – 13 November 2014) was...
mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets of a topological space. A category...
connection Grothendieck construction Grothendieck duality Grothendieck existence theorem Grothendieck fibration Grothendieck's Galois theory Grothendieck group...
In mathematics, the Grothendieck group, or group of differences, of a commutative monoid M is a certain abelian group. This abelian group is constructed...
to those of Ste. Grothendieckspace A generalization which has some of the properties of reflexive spaces and includes many spaces of practical importance...
Alexander Grothendieck. The topology on nuclear spaces can be defined by a family of seminorms whose unit balls decrease rapidly in size. Vector spaces whose...
In mathematics, the Grothendieck inequality states that there is a universal constant K G {\displaystyle K_{G}} with the following property. If Mij is...
major theme has been to study a space by studying sheaves on a space. This idea was expounded by Alexander Grothendieck by introducing the notion of a...
In mathematics, a Grothendieck category is a certain kind of abelian category, introduced in Alexander Grothendieck's Tôhoku paper of 1957 in order to...
Banach space L p ( Ω , μ ) {\displaystyle L^{p}(\Omega ,\mu )} ). Alexander Grothendieck showed that when E {\displaystyle E} is a nuclear space (a concept...
the underlying vector spaces, amongst others the projective cross norm and injective cross norm introduced by A. Grothendieck in 1955. In general, the...
Banach spaces, the so-called 2 3 {\displaystyle {\tfrac {2}{3}}} -nuclear operators. The theorem was proven in 1955 by Alexander Grothendieck. Lidskii's...
theorem holds for ultrabornological spaces. Ultrabornological spaces were introduced by Alexander Grothendieck (Grothendieck [1955, p. 17] "espace du type (β)")...
any space B the groupoid of families over B. The use of these categories fibred in groupoids to describe a moduli problem goes back to Grothendieck (1960/61)...
theory of Grothendieck, which consists, for studying algebraic varieties, of considering as "points", not only the points of the affine space, but also...
Grothendieck connection is a way of viewing connections in terms of descent data from infinitesimal neighbourhoods of the diagonal. The Grothendieck connection...
stratum. Among the several ideals, Grothendieck's Esquisse d’un programme considers (or proposes) a stratified space with what he calls the tame topology...
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