in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

At MFPS 23 at Birmingham, Schröder and Simpson had announced a result that I did not absorb at the time. A special case of that theorem for stably compact spaces was announced by Cohen, Escardo and the author shortly afterwards. I did not believe in the theorem of Schröder and Simpson until I saw a proof that they showed to me in detail during a visit to Edinburgh. At the New Interactions Works...

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

Antoine and Zouaki ([1] and [16]) have given the existence of a continuous selection of (1.1) in the particular case where M − x0 and N − y0 are closed convex cones . In this paper, we extend this result when M (resp. N) approximates continuously its Clarke tangent cone at x0 (resp. y0) (see Definition 2.2). This property is verified at x0 for an important class of sets. We get among others: se...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...