Completeness and Compact Generation in Partially Ordered Sets

Tripled partially ordered sets

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

Partially Ordered Sets

For example, thus far, I had the fortune to work intimately with nine (9) undergraduate students on research questions in the areas of computational algebra and algebraic geometry. I am directing two master’s students in their research for their theses at Sam Houston State University. All of these undergraduate students have enrolled in graduate programs around the country. Three have finished ...

Partially ordered sets and stratification

We employ partially ordered sets to describe the stratification of a social system, using rank to define the strata. We present a simple method of computing the matrix corresponding to the Hasse diagram and prove its correctness. This methodology is applied to analyze the hierarchy of countries that have won at least one Olympic medal. Four different definitions of dominance are given, leading ...

Continuity in Partially Ordered Sets

Broadcasting in Partially Ordered Sets

Let be a partial order on a countable set V such that there exists a minimum element a ∈ V and {u ∈ V : u v} is finite for each v ∈ V . An item of information is to be broadcast to the elements of V according to the policy in the following sense: a is initially informed and broadcasting to v 6= a begins as soon as all elements u ≺ v are informed; the time required to broadcast the information i...