23 citations · 29 across the 9 of their papers we have counts for
9 papers
The sup-inf-completion of a Dedekind complete vector lattice
Eder Kikianty, Luan Naude, Mark Roelands +1
We introduce the sup-inf-completion of a Dedekind complete vector lattice, an essentially unique extension in which every nonempty subset has both a supremum and an infimum. Since…
The Riemann integral on Dedekind complete -algebras
Eder Kikianty, Luan Naude, Mark Roelands +1
In this paper we develop a theory of integration for locally band preserving functions, introduced by Ercan and Wickstead, on Dedekind complete -algebras. Specifically, we const…
Classical theorems from analysis for locally band preserving functions on Dedekind complete -algebras
Eder Kikianty, Luan Naude, Mark Roelands +1
In this paper we explore the concept of locally band preserving functions, introduced by Ercan and Wickstead, on Dedekind complete -algebras. Specifically, we show that all supe…
L-functional analysis
Eder Kikianty, Miek Messerschmidt, Luan Naude +5
Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars or $\mathbb…
On compact packings of Euclidean space with spheres of finitely many sizes
Eder Kikianty, Miek Messerschmidt
For , a compact sphere packing of Euclidean space is a set of spheres in with disjoint interiors so that the contact hypergraph of…
Further results on angular equivalence of norms
Eder Kikianty
Angular equivalence of norms is introduced by Kikianty and Sinnamon (2017) and is a stronger notion than the usual topological equivalence. Given two angularly equivalent norms, if…
Three geometric constants for Morrey spaces
Hendra Gunawan, Eder Kikianty, Yoshihiro Sawano +1
In this paper we calculate three geometric constants, namely the von Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant, for Morrey spaces and discrete Mo…
Angular equivalence of normed spaces
Eder Kikianty, Gord Sinnamon
Angular equivalence is introduced and shown to be an equivalence relation among the norms on a fixed real vector space. It is a finer notion than the usual (topological) notion of…
Discrete Morrey spaces and their generalizations
Hendra Gunawan, Eder Kikianty, Christopher Schwanke
We discuss discrete Morrey spaces and their generalizations, and we prove necessary and sufficient conditions for the inclusion property among these spaces through an estimate for…