We establish a Kollár-type gluing theory for NQC generalized log canonical pairs and use it to prove semi-ampleness results of pairs. As consequences, we the existence flips any pair, show that singularities are Du Bois.

In this paper, we verify the lower semi-continuity and Ekeland’s variational principle for very recent results in a generalized metric space which introduced by Mohamed Jleli Bessem Samet [1]. And sequel obtain certain fixed point theorems related topics.

The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...

The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi-finite thick generalized polygons. We show here that no semi-finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its ...