Approximating Orders in Meet-Continuous Lattices and Regularity Axioms in Many Valued Topology

Abstract

Positron emission tomography (PET) with 2-deoxy-2[(18)F]-fluoro-D-glucose (FDG) can be used to estimate regional cerebral glucose metabolism (rCMRgluc). FDG-PET studies have shown rCMRgluc to be reduced especially in temporal and parietal cortices in Alzheimer's disease (AD). A previous study on monozygotic twins discordant for AD showed that the rCMRgluc of the non-demented twins is reduced significantly in the lateral temporal and parietal cortices compared to unrelated controls. In this study we examined 9 pairs of dizygotic twins discordant for AD with FDG-PET. The rCMRgluc of the demented twins was 16% lower in the prefrontal cortex (p = 0.04), 20% lower in the hippocampus (p = 0.002) and 15% lower in the lateral temporal cortex (p = 0.003) compared to controls. The non-demented twins showed no such reductions on any cortical region compared to unrelated control subjects. This implies that both genes and environment, and not genes alone, are causative in the pathogenesis of AD.

Unified Representability of Total Preorders and Interval Orders through a Single Function: The Lattice Approach

“…Our main reference for general concepts regarding lattices and complete distributivity is [24]. (See also [31] for a more recent reference related to topological properties).…”

-uniform spaces versus -uniform spaces

“…We shall follow the general idea developed in a recent paper [4]. For the reader's convenience we include some details form [4].…”