一致连续偏序集理论

Theories of uniform continuous partial order sets

给出了一致连续偏序集的概念及其性质和等价刻划。利用一致极小集的方法阐述了映射的连续性、保一致小于关系和保一致极小集之间的联系，并证明了完备格是一致连续格当且仅当每个元都存在一致极小集。

The notions of uniform complete partial order sets and uniform continuous partial order sets are defined. The characteristics and properties of uniform continuous partial order sets are investigated.Using the method of the uniform minimal subsets,we explained a few relationships which are among the continunity of the mapping,preserving the uniform way-below relation and the uniform minimal sub-sets. Is is proved that the complete lattices are uniform confinunous if and only if their element exists an uniform subset.