Some characterizations of smoothness

Some Characterizations of Domination

We show that a cocycle has a dominated splitting if and only if there is a uniform exponential gap between singular values of its iterates. Then we consider sets Σ in GL(d, R) with the property that any cocycle with values in Σ has a dominated splitting. We characterize these sets in terms of existence of invariant multicones, thus extending a 2-dimensional result by Avila, Bochi, and Yoccoz. W...

SOME CHARACTERIZATIONS OF HYPER MV -ALGEBRAS

In this paper we characterize hyper MV -algebras in which 0 or1 are scalar elements . We prove that any nite hyper MV -algebra that 0is a scaler element in it, is an MV -algebra. Finally we characterize hyperMV -algebras of order 2 and order 3.

Some results on random smoothness

Based on the analysis of stratification structure on random normed modules, we first present the notion of random smoothness in random normed modules. Then, we establish the relations between random smoothness and random strict convexity. Finally, a type of Gâteaux differentiability is defined for random norms, and its relation to random smoothness is given. The results are helpful in the furth...

Some Characterizations of C(m)

Some Characterizations of Developable Spaces

Two characterizations of developable spaces are proved which may be viewed as analogues, for developable spaces, of the Nagata-Smirnov metrization theorem or of the "double sequence metrization theorem " of Nagata respectively.