The aim of this paper is to set up appropriate uniform convergence spaces in which to reformulate and enrich the Order Completion Method [25] for nonlinear PDEs. In this regard, we consider an appropriate space ML (X) of normal lower semi-continuous functions. The space ML (X) appears in the ring theory of C (X) and its various extensions [15], as well as in the theory of nonlinear, PDEs [25] a...

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

We consider convex sets and functions over idempotent semifields, like the max-plus semifield. We show that if K is a conditionally complete idempotent semifield, with completion K̄, a convex function Kn → K̄ which is lower semi-continuous in the order topology is the upper hull of supporting functions defined as residuated differences of affine functions. This result is proved using a separation...

We put forward a revised definition of stably compact spaces which allows us to show their equivalence with Nachbin’s compact ordered spaces in an entirely elementary fashion. We then exhibit some constructions for stably compact spaces which apparently have not appeared in the literature before. These constructions allow us to show that the set of (sub-)probability valuations can be equipped w...

We obtain the existence of a periodic solution for differential inclusions with lower semi-continuous right-hand sides on non-compact Lie groups. The construction is based combination method guiding functions and technique integral operators parallel translation.