said to be sequentially complete or semi-complete if every Cauchy sequence in S converges to an element in S. X is called sequentially complete if it is...

weakly sequentially complete. Theorem —For every measure μ , {\displaystyle \mu ,} the space L 1 ( μ ) {\displaystyle L^{1}(\mu )} is weakly sequentially complete...

exists a sequentially complete locally convex TVS that is not quasi-complete. If a TVS has a complete neighborhood of the origin then it is complete. Every...

{\displaystyle X.} A topological group is called sequentially complete if it is a sequentially complete subset of itself. Neighborhood basis: Suppose C...

where every Cauchy sequence converges is called sequentially complete; in general, it may not be complete (in the sense that all Cauchy filters converge)...

X} is sequentially bornological or S-bornological, which means that every convex and bornivorous subset of X {\displaystyle X} is sequentially open. where...

quasi-barrelled spaces. There exist sequentially complete Mackey spaces that are not σ-quasi-barrelled. There exist sequentially barrelled spaces that are not...

above theorem: A sequentially complete bounded disk in a Hausdorff TVS is a Banach disk. Any disk in a Hausdorff TVS that is complete and bounded (e.g...

orthocomplementation operation is set complement. Moreover, this lattice is sequentially complete, in the sense that any sequence {Ei}i∈N of elements of the lattice...

topology, the sequential coreflection. In the sequential coreflection, every sequentially-closed set is closed (and every sequentially-open set is open)...

space. A sequentially complete quasibarrelled space. A quasi-complete Hausdorff locally convex infrabarrelled space. A TVS is called quasi-complete if every...

importance for non-metrizable TVSs. Every quasi-complete TVS is sequentially complete. In a quasi-complete locally convex space, the closure of the convex...

In automata theory, sequential logic is a type of logic circuit whose output depends on the present value of its input signals and on the sequence of past...

kp p(x − y). If f is a p-contraction for all p ∈ P and (E, P) is sequentially complete, then f has a fixed point, given as limit of any sequence xn+1 =...

_{i=1}^{n}2^{-i}x_{i}.} In particular, if in addition D {\displaystyle D} is a sequentially complete subset of X , {\displaystyle X,} then this series s ∙ {\displaystyle...

continuous. This includes all topological vector lattices that are sequentially complete. Theorem Let X {\displaystyle X} be an Ordered topological vector...

Chem 12, Chemistry panel, Chemistry screen, SMA 12, SMA 20 and SMAC (Sequential Multiple Analysis - Computer). The tests are performed on machines based...

form of hermaphroditism in fish in nature. About 75% of the 500 known sequentially hermaphroditic fish species are protogynous and often have polygynous...

In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data...

executed concurrently—during overlapping time periods—instead of sequentially—with one completing before the next starts. This is a property of a system—whether...

concerning the result. Assuming that X {\displaystyle X} is weakly sequentially complete Banach space, W. Orlicz proved the following Theorem. If a series...

&{\text{observation}}\end{array}}} the filtering problem is to estimate sequentially the values of the hidden states X k {\displaystyle X_{k}} , given the...

Sequential bargaining (also known as alternate-moves bargaining, alternating-offers protocol, etc.) is a structured form of bargaining between two participants...

even when players participate in multiple mechanisms simultaneously or sequentially. The class of smooth mechanisms – mechanisms that generate approximately...

Every quasi-complete infrabarrelled space is barrelled. A locally convex Hausdorff quasibarrelled space that is sequentially complete is barrelled....

infinite-dimensional spaces, a set that is closed and bounded is not necessarily (sequentially) compact (as is the case in all finite dimensional spaces). Indeed, the...

)} is a locally convex vector lattice that is bornological and sequentially complete, then there exists a family of compact spaces ( X α ) α ∈ A {\displaystyle...

Classical Banach spaces Dual space Reflexive weakly sequentially complete Norm Notes F n {\displaystyle \mathbb {F} ^{n}} F n {\displaystyle \mathbb {F}...

In game theory, a sequential game is defined as a game where one player selects their action before others, and subsequent players are informed of that...

ultrabornological. Every Hausdorff sequentially complete bornological space is ultrabornological. Thus every complete Hausdorff bornological space is ultrabornological...