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groups, the Hahn embedding theorem gives a simple description of all linearly ordered abelian groups. It is named after Hans Hahn. The theorem states that...

the Hahn embedding theorem; the Hahn–Kolmogorov theorem; the Hahn–Mazurkiewicz theorem; the Vitali–Hahn–Saks theorem. Hahn authored the book (Hahn 1921):...

{\displaystyle \mathbb {R} } ). Hahn series were first introduced, as groups, in the course of the proof of the Hahn embedding theorem and then studied by him...

three-lines theorem (complex analysis) Hadwiger's theorem (geometry, measure theory) Hahn decomposition theorem (measure theory) Hahn embedding theorem (ordered...

by Schoenflies in 1905. Abstract algebra Hahn embedding theorem: Every ordered abelian group G order-embeds as a subgroup of the additive group R Ω {\displaystyle...

cannot be embedded in the real numbers, they can be embedded in a power of the real numbers, with lexicographic order, by the Hahn embedding theorem; the example...

w*-topology. This unit ball K is then compact by the Banach–Alaoglu theorem. The embedding j is introduced by saying that for every x ∈ X, the continuous function...

generalisation of this has been recently announced. Cyclically ordered group Hahn embedding theorem Partially ordered group Deroin, Navas & Rivas 2014, 1.1.1. Levi...

the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space...

more. Hahn series are a further (larger) generalization of Puiseux series, introduced by Hans Hahn in the course of the proof of his embedding theorem in...

{\displaystyle \operatorname {dist} (x,Y)\geq 1+\delta } and by the Hahn–Banach theorem there exists a linear form φ ∈ X ′ {\displaystyle \varphi \in X^{\prime...

acceptable in constructive analysis. A famous example of a theorem of this sort is the Hahn–Banach theorem. Every compact metric space (or metrizable space) is...

and Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach theorems from linear functionals (which are always...

can be used to prove the Hahn-Banach theorem and the Alexander subbase theorem. Intuitively, the Boolean prime ideal theorem states that there are "enough"...

under the natural isometric embedding of X {\displaystyle X} into X ″ {\displaystyle X''} given by the Hahn–Banach theorem, the quotient X ′ ′ / X {\displaystyle...

his doctoral dissertation under Hans Hahn's supervision. In it, he established his eponymous completeness theorem regarding first-order logic. He was awarded...

Fyodorov–Schoenflies–Bieberbach theorem Jordan–Schoenflies theorem Schoenflies notation Schoenflies displacement Heine–Borel theorem Arthur Moritz Schoenflies...

induced by Y . {\displaystyle Y.} A topological vector space embedding (abbreviated TVS embedding), also called a topological monomorphism, is an injective...

he chose to go to Vienna to continue his studies. He studied under Hans Hahn and Karl Menger in Vienna, receiving a PhD in 1926. Hurewicz was awarded...

function g on the real line with g(y) ≥ 0. The converse result is Bochner's theorem, stating that any continuous positive-definite function on the real line...