منابع مشابه
Inductively generated formal topologies
Formal topology is today an established topic in the development of constructive, that is intuitionistic and predicative, mathematics. Many classical results of general topology have been already brought into the realm of constructive mathematics by using formal topology and also new light on basic topological notions was gained with this approach which allows distinction which are not sensible...
متن کاملExponentiation of unary topologies over inductively generated formal topologies
We prove that unary formal topologies are exponentiable in the category of inductively generated formal topologies. From an impredicative point of view, this means that algebraic dcpos with a bottom element are exponentiable in the category of open locales.
متن کاملTopologies generated by ideals
A topological space X is said to be generated by an ideal I if for all A ⊆ X and all x ∈ A there is E ⊆ A in I such that x ∈ E, and is said to be weakly generated by I if whenever a subset A of X contains E for every E ⊆ A with E ∈ I, then A itself is closed. An important class of examples are the so called weakly discretely generated spaces (which include sequential, scattered and compact Haus...
متن کاملSpatiality for formal topologies
We define what it means for a formal topology to be spatial, and investigate properties related to spatiality both in general and in examples.
متن کاملTopologies Generated by Closed Intervals
If 〈L, <〉 is a dense linear ordering without end points and A and B disjoint dense subsets of L, then the topology OAB on the set L generated by closed intervals [a, b], where a ∈ A and b ∈ B, is finer than the standard topology, O<, generated by all open intervals and 〈L,OAB〉 is a GO-space. The basic properties of the topology OAB (separation axioms, cardinal functions, metrizability) are inve...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2003
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(03)00052-6