منابع مشابه
Baire Spaces, Sober Spaces
In the article concepts and facts necessary to continue forma-lization of theory of continuous lattices according to [10] are introduced. The notation and terminology used here are introduced in the following papers:
متن کاملSober Spaces and Continuations
A topological space is sober if it has exactly the points that are dictated by its open sets. We explain the analogy with the way in which computational values are determined by the observations that can be made of them. A new definition of sobriety is formulated in terms of lambda calculus and elementary category theory, with no reference to lattice structure, but, for topological spaces, this...
متن کاملBaire Spaces , Sober Spaces 1 Andrzej
In the article concepts and facts necessary to continue formalization of theory of continuous lattices according to [11] are introduced. and [4] provide the notation and terminology for this paper. 1. PRELIMINARIES The following two propositions are true: (1) For all sets X, A, B such that A ∈ Fin X and B ⊆ A holds B ∈ Fin X. (2) For every set X and for every family F of subsets of X such that ...
متن کاملDuality Beyond Sober Spaces: Topological Spaces and Observation Frames
We introduce observation frames as an extension of ordinary frames. The aim is to give an abstract representation of a mapping from observable predicates to all predicates of a specific system. A full subcategory of the category of observation frames is shown to be dual to the category of F! topological spaces. The notions we use generalize those in the adjunction between frames and topological...
متن کاملSober Spaces, Well-Filtration and Compactness Principles
We investigate various notions of sobriety for topological spaces that are equivalent in ZF set theory with the Axiom of Choice but may differ in the absence of choice principles. The Ultrafilter Principle UP (alias Prime Ideal Theorem) suffices for the desired conclusions. We derive from UP three topological postulates and prove their equivalence in ZF without choice: the Well-Filtration Princ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2000
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(98)00089-3