In this paper we will show that partially ordered monads contain sufficient structure for modelling monadic topologies, rough sets and Kleene algebras. Convergence represented by extension structures over partially ordered monads includes notions of regularity and compactness. A compactification theory can be developed. Rough sets [23] are modelled in a generalized setting with set functors. Fu...

In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievableexample is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for thebasis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroidis equivalent to a mapping which satisfies the basis ...

In this paper, some characterizations of fuzzifying strong compactness are given, including in terms nets and presubbases. Several locally the framework topology introduced mapping theorems obtained.

We provide a sufficient condition for the cyclicity of an ordered tensor product L = Va1(ωb1) ⊗ Va2(ωb2) ⊗ . . . ⊗ Vak(ωbk) of fundamental representations of the Yangian Y (g). When g is a classical simple Lie algebra, we make the cyclicity condition concrete, which leads to an irreducibility criterion for the ordered tensor product L. In the case when g = sll+1, a sufficient and necessary cond...