The seminar of the “Order” team will be held on Thursday of each week from 13h to 15h at the Faculty of Sciences of Tunis. The novelty of this year is to encourage the invitation of teachers-researchers from other laboratories than ours.

The sessions will begin on Thursday, September 12, 2019.

The unfinished program is below. It should be completed as participants give their confirmations.

**Thursday, October 3, 2019**

This session will be presential.

Pedro Tradacete Pérez : RECENT PROGRESS ON FREE BANACH LATTICES

Abstract:

The free Banach lattice over a Banach space is introduced and analyzed. This generalizes the concept of free Banach lattice over a set of generators, and allows us to study the Nakano property and the density character of non-degenerate intervals on these spaces, answering some recent questions of B. de Pagter and A.W. Wickstead. Moreover, an example of a Banach lattice which is weakly compactly generated as a lattice but not as a Banach space is exhibited, thus answering a question of J. Diestel.

**Thursday, October 10, 2019**

This session will be by videoconference.

Till Hauser: Order continuity from a topological perspective

Abstract:

We study three types of order convergence and related concepts of order continuous maps in partially ordered sets, partially ordered abelian groups and partially ordered vector spaces, respectively.

An order topology is introduced such that

in the latter two settings under mild conditions order continuity is a topological property.

We present a generalisation of the Ogasawara theorem on the structure of the set of order continuous operators.