【摘要】 本文证明了任给T_O拓扑分子格(L,η),以下三条等价:(1)(L,η)为正则内射拓扑分子格;(2)L为完备集环且其完备余素元集ht(L)形成一连续格,余拓扑η为该连续格ht(L)上的Scott闭集格;(3)存在T_O内射拓扑空间(X,Τ),(L,η)同胚于(P(X),Τ~c)在拓扑分子格范畴中的Sober化。此外,还给出了正则内射拓扑分子格、(一般)内射拓扑分子格以及正则内射分子格的一般结构。作为应用,重新证明了有指数元的拓扑分子格的结构。更多还原

【Abstract】 It is proved in this paper that for a TO topological molecular lattice (L,η), the following conditions are equivalent: (1) (L, η) is a regular injective TO topological molecular lattice; (2) L is a complete set ring and of which the set of complete coprimes forms a continuous lattice, and η is the Scott co-topology on the continuous lattice of complete coprimes; (3) There exists an injective TO space such that (L, η) is homeomorphic to the Soberification (in the sense of topological molecular lattice) of (P(X),TC). Besides, the structures of (not necessarily TO) regular injective topological molecular lattices, the structures of general injective topological molecular lattices and that of regular injective molecular lattices are also given. As applications, a new (and simple) proof of the structures of exponentiable topological molecular lattices is given.更多还原