Further new generalized topologies via mixed constructions due to Császár

On Generalized Injective Spaces in Generalized Topologies

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

Preorder Relators and Generalized Topologies

In this paper we investigate generalized topologies generated by a subbase of preorder relators and consider its application in the concept of the complement. We introduce the notion of principal generalized topologies obtained from the new type of open sets and study some of their important properties.

New cryptographic constructions using generalized LWE

We present first a generalized LWE problem, which is essentially to extend the original LWE to the case of matrices. Then we use this new version of LWE problem, which we call matrix LWE problem to build new cryptographic schemes, which include a new key distribution scheme, a new key exchanges scheme and a new simple identity-based encryption scheme.

On generalized topologies arising from mappings

Given a mapping $f:Xto X$ we naturally associate to it a monotonic map $gg_f:exp Xto exp X$ from the power set of $X$ into itself, thus inducing a generalized topology on $X$. In this paper we investigate some properties of generalized topologies which are defined by such a procedure.

Parsimonious Classification Via Generalized Linear Mixed Models