In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with...

In mathematics, a uniformly bounded family of functions is a family of bounded functions that can all be bounded by the same constant. This constant is...

algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the...

Uniform boundedness conjecture may refer to: Uniform boundedness conjecture for torsion points Uniform boundedness conjecture for rational points Uniform...

holomorphic, then the limit is also holomorphic. The uniform boundedness principle states that a pointwise bounded family of continuous linear operators between...

operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The...

in PN(K), and the general Uniform Boundedness Conjecture says that the number of preperiodic points in PN(K) may be bounded solely in terms of N, the...

In arithmetic geometry, the uniform boundedness conjecture for rational points asserts that for a given number field K {\displaystyle K} and a positive...

operators are closed. Alternatively, it can be argued using the uniform boundedness principle. One relies on the symmetric assumption, therefore the...

the easiest proof uses the non-boundedness of Dirichlet's kernel in L1(T) and the Banach–Steinhaus uniform boundedness principle. As typical for existence...

generalizes the closed graph theorem, the open mapping theorem, and the uniform boundedness principle. The following notation and notions are used, where R :...

Ultrabarrelled space Uniform boundedness principle#Generalisations – Theorem stating that pointwise boundedness implies uniform boundedness Ursescu theorem –...

Hahn–Banach theorem and (independently of Banach and Steinhaus) the uniform boundedness principle. Other theorems include: the Hahn decomposition theorem;...

Patricia Pacelli showed that the Bombieri–Lang conjecture implies a uniform boundedness conjecture for rational points: there is a constant B g , d {\displaystyle...

prove the open mapping theorem, the closed graph theorem and the uniform boundedness principle. BCT1 also shows that every nonempty complete metric space...

of rational maps, and her recent proof (with DeMarco and Ye) of uniform boundedness results for numbers of torsion points on families of bielliptic genus...

normability criterion – Characterization of normable spaces Local boundedness Totally bounded space – Generalization of compactness Narici & Beckenstein 2011...

under f {\displaystyle f} is bounded. The following theorem relates local boundedness of functions with the local boundedness of topological vector spaces:...

d\mu }=\int _{S}{f\,d\mu }.} Remark: The pointwise convergence and uniform boundedness of the sequence can be relaxed to hold only μ-almost everywhere,...

is dense in X . {\displaystyle X.} A special case of this is the uniform boundedness principle. The empty space is a Baire space. It is the only space...

a bounded set in Y {\displaystyle Y} .[citation needed] Weaker than boundedness is local boundedness. A family of bounded functions may be uniformly bounded...

mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally bounded set can be covered...

In mathematics, uniform integrability is an important concept in real analysis, functional analysis and measure theory, and plays a vital role in the...

satisfied by a uniformly bounded sequence { fn } of differentiable functions with uniformly bounded derivatives. Indeed, uniform boundedness of the derivatives...

continuous T-periodic function need not converge pointwise. The uniform boundedness principle yields a simple non-constructive proof of this fact. In...

Every weakly convergent sequence {xn} is bounded, by the uniform boundedness principle. Conversely, every bounded sequence in a Hilbert space admits weakly...

implies χ ( R / P , R / Q ) > 0 {\displaystyle \chi (R/P,R/Q)>0} . Uniform boundedness conjecture for rational points: do algebraic curves of genus g ≥...

Ursescu theorem – Generalization of closed graph, open mapping, and uniform boundedness theorem Webbed space – Space where open mapping and closed graph...

operators from X {\displaystyle X} to Y . {\displaystyle Y.} The uniform boundedness principle states that if for all x {\displaystyle x} in X {\displaystyle...

then A is countable, and it can be denoted as {an: n∈N}. By the uniform boundedness of (fn)n ∈ N and B-W theorem, there is a subsequence (f(1)n)n ∈ N...