On Lattices of Uniformities

We study lattice theoretical properties of lattices of uniformities such as modularity, distributive laws and the existence of (relative) complements. For this the concepts of permutable uniformities (see Definition 3.1) and independent uniformities (see Definition 4.1) are important. Moreover, we show that e.g. the lattice of all lattice uniformities on a lattice L is a closed sublattice of the lattice of all uniformities on L.     

TL—子环上的TL—子模的格

研究TL－子环上TL－子模形成的格及其子格的性质,给出这些格之间的同态与同构定理。     

Distributivity and stationary reflections

In this paper, we present some relations between generalized distributivity of quotient algebras and Mahlo operations, and show that the distributivity implies some variants of stationary relections.

     

Partition numbers

We continue [21] and study partition numbers of partial orderings which are related to (ω)/fin. In particular, we investigate P_f, be the suborder of ((ω)/fin)^ω containing only filtered elements, the Mathias partial order M, and (ω), (ω)^ω the lattice of (infinite) partitions of ω, respectively. We show that Solomon's inequality holds for M and that it consistently fails for P_f. We show that the partition number of (ω) is C. We also show that consistently the distributivity number of (ω)^ω is smaller than the distributivity number of (ω)/fin. We also investigate partitions of a Polish space into closed sets. We show that such a partition either is countable or has size at least D, where D is the dominating number. We also show that the existence of a dominating family of size ₁ does not imply that a Polish space can be partitioned into ₁ many closed sets.     

Remarks on the lattices of fuzzy subsets of a groupoid

In this paper we give a necessary and sufficient condition for a groupoid D such that the sup-min product is distributive over arbitrary intersection of fuzzy subsets of D, and correct some results from the paper [S. Ray, The lattice of all idempotent fuzzy subsets of a groupoid, Fuzzy Sets and Systems 96 (1998) 239–245]. Also, we prove that the set of all idempotent fuzzy sets forms a complete lattice, which is a complete join-sublattice of the lattice of all fuzzy subgroupoids. This result extends the corresponding result from the above mentioned paper.     

Some observations on fuzzy relations over fuzzy subsets

This paper considers fuzzy relations defined over fuzzy subsets and settles some open problems regarding the distributivity and transitivity of such relations     

WBR0-代数的构建与性质

通过对WBR0-代数中各条件的研究,首先讨论它们之间的独立性,进而将WBR0-代数进行简化.其次讨论WBR0-代数的性质及其分配性,并构造一个非BR0 -代数的WBR0-代数的结构说明了WBR0-代数不同于BR0-代数.同时该结构说明WBR0-代数不满足分配律.     

Characterization of distributivity in a solid

We give a characterization of the validity of the distributive law in a solid. There exists equivalence between the characterization and the modified axiom of distributivity valid in a solid.