Maximal spaceability in sequence spaces

Spaceability on Morrey Spaces

In this paper, as a main result for Morrey spaces, we prove that the set $mathcal M_q^p(mathbb R^n)backslashbigcup_{q<rleq p}mathcal M_r^p(mathbb R^n)$ is spaceable in $mathcal M_q^p(mathbb R^n)$, where $0<q<p<infty$.}

Maximal pseudocompact spaces

Maximal pseudocompact spaces (i.e. pseudocompact spaces possessing no strictly stronger pseudocompact topology) are characterized. It is shown that submaximal pseudocompact spaces whose pseudocompact subspaces are closed need not be maximal pseudocompact. Various techniques for constructing maximal pseudocompact spaces are described. Maximal pseudocompactness is compared to maximal feeble compa...

A New Class of Banach Sequence Spaces

Sequence of maximal distance codes in graphs or other metric spaces

Given a subset C in a metric space E, its successor is the subset s(C) of points at maximum distance from C in E. We study some properties of the sequence obtained by iterating this operation. Graphs with their usual distance provide already typical examples.

Orbits of Maximal Vector Spaces

Let V∞ be a standard computable infinite-dimensional vector space over the rationals. The lattice L(V∞) of computably enumerable vector subspaces of V∞, and its quotient lattice modulo finite dimension, L(V∞), have been extensively studied. However, many important questions still remain open. In 1998, R. Downey and J. Remmel posed the question of finding meaningful orbits in L(V∞) (Question 5.8...