scholarly journals Split Hausdorff internal topologies on posets

2019 ◽  
Vol 17 (1) ◽  
pp. 1756-1763
Author(s):  
Shuzhen Luo ◽  
Xiaoquan Xu
Keyword(s):  
Binary Relation ◽  
Interval Topology

Abstract In this paper, the concepts of weak quasi-hypercontinuous posets and weak generalized finitely regular relations are introduced. The main results are: (1) when a binary relation ρ : X ⇀ Y satisfies a certain condition, ρ is weak generalized finitely regular if and only if (φρ(X, Y), ⊆) is a weak quasi-hypercontinuous poset if and only if the interval topology on (φρ(X, Y), ⊆) is split T2; (2) the relation ≰ on a poset P is weak generalized finitely regular if and only if P is a weak quasi-hypercontinuous poset if and only if the interval topology on P is split T2.

The Formation of the Binary Structure in Early Rabbinic Literature

2018 ◽  
Author(s):  
Adi Ophir ◽  
Ishay Rosen-Zvi
Keyword(s):  
Detailed Analysis ◽  
Binary Relation ◽  
Rabbinic Literature ◽  
Binary Structure ◽  
Binary Formation

This chapter sets the stage for a detailed analysis of the rabbinic goy. It traces the consolidation of the binary relation and the exclusion of hybrid categories. It further traces the rabbinic tendency to erase intermediate categories (Samaritans; foreign slaves; God-fearers; heretics) and force them into the new binary formation. From this perspective a new reading of the conversion ceremony is also offered. First appearing in rabbinic literature, the ceremony transformed diffusive spaces of conversion into a sharp and unequivocal procedure of passage—a transitory, instant event. Instead of reading this procedure as an evidence of a permeable border between groups, as scholars tend to do, the chapter shows how it performs the very erection of this border as it regulates its crossing.

scholarly journals Hermes: a simple and efficient algorithm for building the AOC-poset of a binary relation

2014 ◽  
Vol 72 (1-2) ◽  
pp. 45-71 ◽  
Author(s):  
Anne Berry ◽  
Alain Gutierrez ◽  
Marianne Huchard ◽  
Amedeo Napoli ◽  
Alain Sigayret
Keyword(s):  
Binary Relation ◽  
Efficient Algorithm

Quotient groups and realization of tight Riesz groups

1973 ◽  
Vol 16 (4) ◽  
pp. 416-430 ◽  
Author(s):  
John Boris Miller
Keyword(s):  
Normal Subgroup ◽  
Open Interval ◽  
Canonical Homomorphism ◽  
Interval Topology ◽  
Essential Step ◽  
Image Position ◽  
Quotient Groups

Let (G, ≼) be an l-group having a compatible tight Riesz order ≦ with open-interval topology U, and H a normal subgroup. The first part of the paper concerns the question: Under what conditions on H is the structure of (G, ≼, ∧, ∨, ≦, U) carried over satisfactorily to by the canonical homomorphism; and its answer (Theorem 8°): H should be an l-ideal of (G, ≼) closed and not open in (G, U). Such a normal subgroup is here called a tangent. An essential step is to show that ≼′ is the associated order of ≦′.

scholarly journals Object-Free Definition of Categories

2013 ◽  
Vol 21 (3) ◽  
pp. 193-205
Author(s):  
Marco Riccardi
Keyword(s):  
Binary Relation ◽  
Category Theory ◽  
Final Part ◽  
One To One ◽  
Definition Of

Summary Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach that does not refer to objects as elements of the theory, and are usually indicated as object-free category [1] or as arrowsonly category [16]. In this article is proposed a new definition of an object-free category, introducing the two properties: left composable and right composable, and a simplification of the notation through a symbol, a binary relation between morphisms, that indicates whether the composition is defined. In the final part we define two functions that allow to switch from the two definitions, with and without objects, and it is shown that their composition produces isomorphic categories.

On the H -Ordered Interval Topology

1968 ◽  
Vol s1-43 (1) ◽  
pp. 517-520
Author(s):  
S. D. McCartan
Keyword(s):  
Interval Topology

scholarly journals Introduction to Formal Preference Spaces

2013 ◽  
Vol 21 (3) ◽  
pp. 223-233
Author(s):  
Eliza Niewiadomska ◽  
Adam Grabowski
Keyword(s):  
Binary Relation ◽  
Preference Relation ◽  
Consumer Preference ◽  
Consumer Theory ◽  
Mathematical Economics ◽  
Characteristic Relation ◽  
Finite Set ◽  
Preference Structures ◽  
Equal Interest

Summary In the article the formal characterization of preference spaces [1] is given. As the preference relation is one of the very basic notions of mathematical economics [9], it prepares some ground for a more thorough formalization of consumer theory (although some work has already been done - see [17]). There was an attempt to formalize similar results in Mizar, but this work seems still unfinished [18]. There are many approaches to preferences in literature. We modelled them in a rather illustrative way (similar structures were considered in [8]): either the consumer (strictly) prefers an alternative, or they are of equal interest; he/she could also have no opinion of the choice. Then our structures are based on three relations on the (arbitrary, not necessarily finite) set of alternatives. The completeness property can however also be modelled, although we rather follow [2] which is more general [12]. Additionally we assume all three relations are disjoint and their set-theoretic union gives a whole universe of alternatives. We constructed some positive and negative examples of preference structures; the main aim of the article however is to give the characterization of consumer preference structures in terms of a binary relation, called characteristic relation [10], and to show the way the corresponding structure can be obtained only using this relation. Finally, we show the connection between tournament and total spaces and usual properties of the ordering relations.

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