in this paper,  the concept of fuzzy metric-like spaces is introduced which generalizes  the notion of fuzzy metric spaces given by george and veeramani cite{vee1}. some fixed point results for fuzzy contractive mappings on fuzzy metric-like spaces are derived. these results generalize several comparable results from the current literature. we also provide illustrative examples in support of ou...

variety). For each i, let φi(x) be a C-dense quantifier-free Li-formula with parameters from K. Then we can find a K-definable rational function f : C → P which is non-constant, and has the property that the divisor f−1(0) is a sum of distinct points in ⋂n i=1 φi(K), with no multipliticities. (In particular, the support of the divisor contains no points from C(K)\C(K) and no points from C \ C.)...

We study analytic Zariski structures from the point of view of non-elementary model theory. We show how to associate an abstract elementary class with a one-dimensional analytic Zariski structure and prove that the class is stable, quasi-minimal and homogeneous over models. We also demonstrate how Hrushovski’s predimension arises in this general context as a natural geometric notion and use it ...

The notion of an analytic Zariski structure was introduced in [1] by the author and N.Peatfield in a form slightly different from the one presented here. Analytic Zariski generalises the previously known notion of a Zariski structure (see [2] for one-dimensional case and [3], [4] for the general definition) mainly by dropping the requirement of Noetherianity and weakening the assumptions on the...

Abstract We prove that the base space of a log smooth family canonical pairs general type is as well algebraically degenerate, when admits relative good minimal model over Zariski open subset and maximal variation.

Let G be SLn, Sp2n or SOn. We consider the moduli space M of semistable principal G-bundles over a curve X . Our main result is that if U is a Zariski open subset of M then there is no universal bundle on U × X .

Abstract We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite-dimensional Hermitian symmetric spaces, which allows us to maximal representations. When the target is not tube type, we show that there cannot be Zariski-dense representations, whenever existence boundary map can guaranteed, representation preserves finite-dimensional totally geodesic s...