论文标题
矩形晶格的拓扑二元性
Topological duality for orthomodular lattices
论文作者
论文摘要
描述了一类有序的关系拓扑空间，我们称之为矫形空间。我们对这些空间的构建涉及在Hartonas引入的一类拓扑框架中添加拓扑，并按照Bimbó的拓扑化对Goldblatt在代表Ortholattices代表的正面形式的拓扑化。然后，我们证明了正数晶格和同态的类别双重等同于矫形空间的类别和某些连续的框架形态，我们称之为连续的弱p固态。众所周知，矫码晶格为量子逻辑q提供了代数语义。因此，作为我们二元性的应用，我们使用正数空间为Q开发了一种拓扑语义，并证明了声音和完整性。
A class of ordered relational topological spaces is described, which we call orthomodular spaces. Our construction of these spaces involves adding a topology to the class of orthomodular frames introduced by Hartonas, along the lines of Bimbó's topologization of the class of orthoframes employed by Goldblatt in his representation of ortholattices. We then prove that the category of orthomodular lattices and homomorphisms is dually equivalent to the category of orthomodular spaces and certain continuous frame morphisms, which we call continuous weak p-morphisms. It is well-known that orthomodular lattices provide an algebraic semantics for the quantum logic Q. Hence, as an application of our duality, we develop a topological semantics for Q using orthomodular spaces and prove soundness and completeness.
