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...

Many of the definitions and results concerning connected im kleinen continua become useful only when these continua are locally compact. This is especially true in the cyclic element theory. For if a continuous curve M is not locally compact, it is not necessarily true that a simple closed curve in M belongs to a cyclic element of M. Furthermore, if a continuous curve M is not locally compact, ...

let s be a locally compact topological foundation semigroup with identity and ma(s) be its semigroup algebra. in this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $m_a(s)$ of a locally compact topological foundationsemigroup with identity.