In the present paper, we define regularity and normality like strong S1 regularity, S1 regularity, weak S1 regularity, strong S1 normality, S1 normality as well as weak S1 normality on L-topological spaces. Also we investigate some of their properties and the relations between them. 2010 Mathematics Subject Classification: 54A40, 54D10, 54D15, 54D65, 03E72.

We shall discuss further regularity properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we pre...

The one-to-one relation between the points fulfilling the KKT conditions of an optimization problem and the zeros of the corresponding Kojima function is well-known. In the present paper we study the interplay between metric regularity and strong regularity of this a priori nonsmooth function in the context of semidefinite programming. Having in mind the topological structure of the positive se...

We define strong regularity of a parametric interval matrix and give conditions that characterize it. The new conditions give a better estimation for regularity of a parametric matrix than the conditions used so far. Verifiable sufficient regularity conditions are also presented for parametric matrices. The new sufficient conditions motivate a generalization of Rump’s parametric fixed-point ite...

valdis laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. in this paper we introduce a new property of acts over monoids, called u-wpf which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. we also show that regu...

We consider a parabolic equation with a drift term u+b∇u−ut = 0. Under the condition divb = 0, we prove that solutions possess dramatically better regularity than those provided by standard theory. For example, we prove continuity of solutions when not even boundedness is expected.

We shall continue to discuss further properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we pr...