A final remark on extending to strict total orders in modules

Extending Partial Orders on O-minimal Structures to Deenable Total Orders

Extending Partial Orders on o-Minimal Structures to Definable Total Orders

In this note we answer a question raised by John Truss. He asked if every definable partial ordering in an o-minimal structure can be extended to a definable total order. His question is motivated by analogy with the Order Extension Principle, a weak choice-like axiom of interest to set theorists, which asserts that every partial ordering of a set can be extended to a total order of the set (se...

Extending Partial Orders to Dense Linear Orders

A Remark on Total Domination Critical Graphs

A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G− v is less than the total domination number of G. We call these graphs γt-critical. In this paper, we disprove a conjecture posed in a recent paper(On an open problem concerning total domination critical graphs, Expo. Mat...

Strict Isometries of Arbitray Orders

We consider the elementary operator L, acting on the Hilbert-Schmidt Class C2(H), given by L(T ) = ATB, with A and B bounded operators on a separable Hilbert space H. In this paper we establish results relating isometric properties of L with those of the defining symbols A and B. We also show that if A is a strict n−isometry on a Hilbert space H then {I, A∗A, (A∗)2A2, . . . , (A∗)n−1An−1} is a ...