Studia Logica 43 (4):341 - 351 (1984)
|Abstract||This paper is closely related to investigations of abstract properties of basic logical notions expressible in terms of closure spaces as they were begun by A. Tarski (see ). We shall prove many properties of -conjunctive closure spaces (X is -conjunctive provided that for every two elements of X their conjunction in X exists). For example we prove the following theorems:1. For every closed and proper subset of an -conjunctive closure space its interior is empty (i.e. it is a boundary set). 2. If X is an -conjunctive closure space which satisfies the -compactness theorem and [X] is a meet-distributive semilattice (see ), then the lattice of all closed subsets in X is a Heyting lattice. 3. A closure space is linear iff it is an -conjunctive and topological space. 4. Every continuous function preserves all conjunctions.|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Francisco Zapata & Vladik Kreinovich (2012). Reconstructing an Open Order From Its Closure, with Applications to Space-Time Physics and to Logic. Studia Logica 100 (1-2):419-435.
Andrzej W. Jankowski (1986). Some Modifications of Scott's Theorem on Injective Spaces. Studia Logica 45 (2):155 - 166.
Michael Huemer (2005). Logical Properties of Warrant. Philosophical Studies 122 (2):171 - 182.
Josep M. Font & Ventura Verdú (1993). The Lattice of Distributive Closure Operators Over an Algebra. Studia Logica 52 (1):1 - 13.
Andrzej W. Jankowski (1985). Galois Structures. Studia Logica 44 (2):109 - 124.
Jarosław Achinger (1986). On a Problem of P(Α, Δ, Π) Concerning Generalized Alexandroff S Cube. Studia Logica 45 (3):293 - 300.
Jarosław Achinger (1986). Generalization of Scott's Formula for Retractions From Generalized Alexandroff's Cube. Studia Logica 45 (3):281 - 292.
Andrzej W. Jankowski (1986). Retracts of the Closure Space of Filters in the Lattice of All Subsets. Studia Logica 45 (2):135 - 154.
Andrzej W. Jankowski (1985). Disjunctions in Closure Spaces. Studia Logica 44 (1):11 - 24.
Andrzej W. Jankowski (1985). Universality of the Closure Space of Filters in the Algebra of All Subsets. Studia Logica 44 (1):1 - 9.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads3 ( #203,804 of 556,802 )
Recent downloads (6 months)1 ( #64,847 of 556,802 )
How can I increase my downloads?