论文标题
自由代数在定向空间上
Free algebras over directed spaces
论文作者
论文摘要
定向空间是域理论中DCPO的自然拓扑扩展，并形成笛卡尔封闭类别。为了对非确定语义进行建模，通过自由代数的形式定义了定向空间上的功率结构。我们表明，伴随函子定理存在任何有向空间上的自由代数。 C空间（分别\ b空间）可以被描述为连续的（分别\代数）定向空间。我们表明，连续空间只是通过拓扑理想的所有代数空间的缩回，这是圆形理想的概括。此外，通过分类方法，我们表明在连续（分别\代数）空间上自由代数的载体空间仍然是连续的（resp。\代数）空间。
Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. In order to model nondeterministic semantics, the power structures over directed spaces were defined through the form of free algebras. We show that free algebras over any directed space exist by the Adjoint Functor Theorem. An c-space (resp.\ b-space) can be characterized as a continuous (resp.\ algebraic) directed space. We show that continuous spaces are just all retracts of algebraic spaces by means of topological ideals, which are generalizations of the rounded ideals. Moreover, by categorical methods, we show that the carrier spaces of free algebras over continuous (resp.\ algebraic) spaces are still continuous (resp.\ algebraic) spaces.
