A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions all into one big algebra, the “Cartan Calculus”. (This is an extended versio...

Several generalized Wallman type spaces are considered as well as various lattices of subsets therein. In particular, regularity of these lattices and consequences are investigated. Also considered are necessary and sufficient conditions for these lattices to be Lindel6f as well as replete, prime complete, and fully replete.

We prove the existence of designs of small size in a number of contexts. In particular our techniques can be applied to prove the existence of ndesigns on S of size Od(n d log(n)d−1).

A separable Banach space X contains l1 isomorphically if and only if X has a bounded fundamental total wc∗0-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total wc∗0-biorthogonal system.

In this article we introduce the difference double sequence spaces 2`∞(∆, q), 2c(∆, q), 2c0(∆, q), 2c(∆, q), 2c0 (∆, q), 2c (∆, q) and 2c0 (∆, q) defined over a seminormed space (X, q), seminormed by q. We examine some topological and algebraic properties of these spaces like symmetricity, solidness, monotonocity, convergence free, nowhere densenes etc. We prove some inclusion results too.

In this paper, we obtain the existence and the uniqueness of common best proximity point theorems for non-self mappings between two subsets of a complex valued metric space satisfying certain contractive conditions. Our results supported by some examples.

To be written.

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