The first point here is that convex sets can be separated by linear functionals. Second, continuous linear functionals on subspaces of a locally convex topological vectorspace have continuous extensions to the whole space. Proofs are for real vectorspaces. The complex versions are corollaries. A crucial corollary is that on locally convex topological vectorspaces continuous linear functionals s...

Given f : X → R ∪ {+∞} a convex and lower semi-continuous function defined on a reflexive Banach space X, and L, a closed linear manifold of X over which f takes at least a real value, the aim of this note is to prove the following Baire category result: in the Euclidean setting, the set of affine functions dominated by f on L for which there is no dominated extension to X is always of first Ba...

Given such a series a = ∑ γ aγt γ ∈ K and α ∈ Γ we can truncate the series at t to give the series a|α := ∑ γ<α aγt γ ∈ K. We call a|α a truncation of a; if in addition a 6= a|α (equivalently, α 6 β for some β ∈ supp a), then a|α is said to be a proper truncation of a. Thus all truncations of a are proper iff supp a is cofinal in Γ. The only proper truncation of ct with nonzero c ∈ k is 0. A su...

Modern Concepts & Developments in Agronomy Analysis with a Dendrometer of Pruned Mango Trees Federico Hahn* and MI Jesús García Martínez Department Irrigation, Universidad Autonoma Chapingo, Texcoco, México *Corresponding author: Hahn, Submission: March 24, 2022 Published: April 21, DOI: 10.31031/MCDA.2022.10.000746 ISSN 2637-7659Volume10 Issue 5