拓扑效应代数

Topological effect algebras

在一些经典效应代数上引入了拓扑结构,使其成为拓扑效应代数,证明了两个拓扑效应代数的直和仍是拓扑效应代数,拓扑效应代数的模糊集系统仍是拓扑效应代数。给出了拓扑效应代数上连续映射的定义,并研究了拓扑效应代数上态射(单调态射、同构)的连续性,证明了从一个拓扑效应代数到另一个拓扑效应代数的全体连续映射之集仍是拓扑效应代数。

Topological structure is introduced on some classic effect algebras, and so the effect algebras become topological effect algebras. We prove that the direct sum of two topological effect algebras is still topological effect algebra, and the fuzzy system of topological effect algebra is still topological effect algebra. Continious map between topological effect algebras are given, and the continuity of morphisms, monomorphisms and isomorphic are discussed. Finally, it is proved that the set of all continious maps from a topological effect algebra to another is also a topological effect algebra.