Unilateral and Bilateral Characterizations of Increasing and Strictly Increasing Maps

Luc Barbet (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We define and study various properties of lateral increasing for mappings defined between two ordered spaces. After introducing some particular classes of ordered spaces, we formulate unilateral characterizations of the property of increasing. The main theorem characterizes the increasing of a map defined on a complete totally ordered space with bilateral conditions which generalize the classical notions of right or left increasing [1]. Finally, many characterizations of strictly increasing maps are established.

Mots clés: characterization of isotone (order-preserving; increasing) and strictly isotone maps; left and right isotone maps; totally ordered spaces; complete ordered spaces

Domaines: Topologie générale [math.GN]

Luc Barbet. Unilateral and Bilateral Characterizations of Increasing and Strictly Increasing Maps. 2006. ⟨hal-00423387⟩