The following two assertions are equivalent for an o-minimal expansion of ordered group $\mathcal M=(M,<,+,0,\ldots)$. There exists a definable bijection between bounded interval and unbounded interval. Any continuous function $f:A \rightarrow M$ defined on closed subset $M^n$ has extension $F:M^n M$.

In this paper we investigate Multi-Objective Integer Linear Programming (MOILP) problems with unbounded feasible region and introduce recession direction for MOILP problems. Then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of MOILP problems. Finally we present some examples with unbounded feasible region and fi...

We extend the basic axiomatization of interval convex relations by Allen and Hayes with unbounded intervals. Unbounded intervals include since intervals with a finite beginning point and infinite ending point, until intervals with an infinite beginning point and finite ending point and the constant alltime representing the whole time line, with both extreme points being infinite. A number of re...

Definition 1. Let f and g be functions in ω. We say that f is dominated by g iff there is some natural number n such that f ≤n g, i.e. (∀i ≥ n)(f(i) ≤ g(i)). Then <∗= ∪ ≤n is called the bounding relation on ω. If F is a family of functions in ω we say that F is dominated by the function g, and denote it by F <∗ g iff (∀f ∈ F)(f <∗ g). We say that F is unbounded (also not dominated) iff there is...