Locally Thin Set Families

A Better Bound for Locally Thin Set Families

A family of subsets of an n-set is 4-locally thin if for every quadruple of its members the ground set has at least one element contained in exactly 1 of them. We show that such a family has at most 2 members. This improves on our previous results with Noga Alon. The new proof is based on a more careful analysis of the self-similarity of the graph associated with such set families by the graph ...

Infinite Dimensional Families of Locally Nonsolvable Partial Differential Operators

Local solvability is analyzed for natural families of partial differential operators having double characteristics. In some families the set of all operators that are not locally solvable is shown to have both infinite dimension and infinite codimension.

TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

Some Results on Boundedness in Locally Convex Cones

Fuzzy $bigwedge_{e}$ Sets and Continuity in Fuzzy Topological spaces

We introduce a new class of fuzzy open sets called fuzzy $bigwedge_e$ sets which includes the class of fuzzy $e$-open sets. We also define a weaker form of fuzzy $bigwedge_e$ sets termed as fuzzy locally $bigwedge_e$ sets. By means of these new sets, we present the notions of fuzzy $bigwedge_e$ continuity and fuzzy locally $bigwedge_e$ continuity which are weaker than fuzzy $e$-continuity and f...