Lexicographic product decompositions of a linearly ordered group

Semidirect Product Decompositions of Ordered Groupoids and Inverse Semigroups

Linearly Ordered Topological Spaces

This work is devoted to the study of certain cardinality modifications of paracompactness and compactness in the setting of linearly ordered spaces. Some of the concepts treated here have previously been studied by Aquaro [l]1, Gulden [4], Kennison [5], Mansfield [6], Morita [7], and Poppe [9]. On the other hand, the concept of m-boundedness, introduced in §2, is new. Our main results (Theorems...

Quasimartingales with a Linearly Ordered Index Set

We consider quasi-martingales indexed by a linearly order set. We show that such processes are isomorphic to a given class of (finitely additive) measures. From this result we easily derive the classical theorem of Stricker as well as the decompositions of Riesz, Rao and the supermartingale decomposition of Doob and Meyer.

Lexicographic Product of Extendable Graphs

Lexicographic product G◦H of two graphs G and H has vertex set V (G)×V (H) and two vertices (u1, v1) and (u2, v2) are adjacent whenever u1u2 ∈ E(G), or u1 = u2 and v1v2 ∈ E(H). If every matching of G of size k can be extended to a perfect matching in G, then G is called k-extendable. In this paper, we study matching extendability in lexicographic product of graphs. The main result is that the l...

Cayley digraphs and lexicographic product ∗

In this paper, we prove that a Cayley digraph Γ = Cay(G, S) is a nontrivial lexicographical product if and only if there is a nontrivial subgroup H of G such that S \ H is a union of some double cosets of H in G.