Syntactical Proof of Translation and Separation Theorems on Subsystems of Elementary Ontology

1991 ◽  
Vol 37 (9-12) ◽  
pp. 129-138 ◽  
Author(s):  
Mitio Takano
Keyword(s):  
Separation Theorems ◽  
Elementary Ontology

scholarly journals Horosphere slab separation theorems in manifolds without conjugate points

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Sameh Shenawy
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Conjugate Points ◽  
Separation Theorems ◽  
Farthest Points ◽  
Simply Connected ◽  
Convex Subsets

Abstract Let $\mathcal {W}^{n}$ W n be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let $W\in \mathcal {W}^{n}$ W ∈ W n and let A and B be two convex subsets of W. This note aims to investigate separation and slab horosphere separation of A and B. For example,sufficient conditions on A and B to be separated by a slab of horospheres are obtained. Existence and uniqueness of foot points and farthest points of a convex set A in $W\in \mathcal {W}$ W ∈ W are considered.

scholarly journals Real closed separation theorems and applications to group algebras

2013 ◽  
Vol 263 (2) ◽  
pp. 435-452 ◽  
Author(s):  
Tim Netzer ◽  
Andreas Thom
Keyword(s):  
Group Algebras ◽  
Separation Theorems
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