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

Bundles of matrix pencils (under strict equivalence) are sets having the same Kronecker canonical form, up to eigenvalues (namely, they an infinite union orbits under equivalence). The notion bundle for was introduced in 1990's, following matrices similarity, by Arnold 1971, and it has been extensively used since then. Despite amount literature devoted describing topology bundles pencils, some ...

The Yang-Baxter equation plays a fundamental role in various areas of mathematics. Its solutions, called braidings, are built, among others, from Yetter-Drinfeld modules over a Hopf algebra, from self-distributive structures, and from crossed modules of groups. In the present paper these three sources of solutions are unified inside the framework of Yetter-Drinfeld modules over a braided system...

This paper proposes a compositional model-theoretic account of the way the interpretation of indicative conditionals is determined and constrained by the temporal and modal expressions in their constituents. The main claim is that the tenses in both the antecedent and the consequent of an indicative conditional are interpreted in the same way as in isolation. This is controversial for the antec...

links the clauses “you need anything” and “I’m Jill” in a conditional construction, but semantically we may naturally perceive the propositions expressed by these clauses as conditionally unrelated; the name of the woman does not depend on whether the addressee needs anything or not. To humorously misapprehend such conditional sentences, as Martin does, is to pretend to see a conditional relati...