Orderings of filters in terms of reloids ∗ Extensions of
Orderings of filters which extend Rudin-Keisler preorder of ultrafilters are described in terms of reloids that (roughly speaking) is filters on sets of binary relations between some sets. Also it is defined isomorphism of filters which extends Rudin-Keisler equivalence of ultrafilters.
Funcoids and Reloids
It is a part of my Algebraic General Topology research. In this article I introduce the concepts of funcoids which generalize proximity spaces and reloids which generalize uniform spaces. The concept of funcoid is generalized concept of proximity, the concept of reloid is cleared from superfluous details (generalized) concept of uniformity. Also funcoids and reloids are generalizations of binary relations whose domains and ranges are filters (instead of sets). Also funcoids and reloids can be considered as a generalization of (oriented) graphs, this provides us with a common generalization of analysis and discrete mathematics. The concept of continuity is defined by an algebraic formula (instead of old messy epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially ordered category. In one formula are generalized continuity, proximity continuity, and uniform continuity.
A Hopewellian Burial Site in the Lower Republican Valley, Kansas
The senior author has for a number of years worked on the problem of the numerous and virtually unknown burial sites on the bluffs bordering the valley of the Republican River in Geary and Clay Counties, Kansas. This work has been a matter of some urgency, owing to the prevalence of unsystematic amateur excavation on the more prominent stone cairns found in the area. Fortunately, the complete excavation of the larger cairns involves too much labor for the merely curious, and it has often been possible to salvage material and information despite disturbance.