Topologies on totally ordered sets

The Number of Convex Topologies on a Finite Totally Ordered Set

We give an algorithm to find the number Tcvx(n) of convex topologies on a totally ordered set X with n elements, and present these numbers for n ≤ 10. 2010 Mathematics Subject Classification: 54A10, 54F05, 06F30, 05A15.

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.

Sublattices of Lattices of Order-Convex Sets, III: The Case Of Totally Ordered Sets

For a partially ordered set P , let Co(P ) denote the lattice of all order-convex subsets of P . For a positive integer n, we denote by SUB(LO) (resp., SUB(n)) the class of all lattices that can be embedded into a lattice of the form ∏

Totally Ordered Commutative Semigroups

Let 5( + , < ) be a system consisting of a set S endowed with an associative binary operation + and a total ( = linear = simple) order relation < . The composition + and the relation < may be connected by either or both of the following conditions. MC (Monotone Condition). If a and b are elements of 5 such that ax+y ...

Signed Interval Logi on Totally Ordered Domains