Extensional Confluences and Local Closure Operators

2015 ◽  
pp. 128-144 ◽  
Author(s):  
Henry Soldano
Keyword(s):  
Closure Operators ◽  
Local Closure

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

2021 ◽  
Vol 179 (1) ◽  
pp. 59-74
Author(s):  
Josef Šlapal
Keyword(s):  
Direct Product ◽  
Jordan Curve ◽  
Closure Operator ◽  
Jordan Curve Theorem ◽  
Closure Operators ◽  
Ternary Relation ◽  
Digital Space ◽  
Jordan Curves ◽  
Curves And Surfaces ◽  
Digital Plane

In this paper, we propose new definitions of digital Jordan curves and digital Jordan surfaces. We start with introducing and studying closure operators on a given set that are associated with n-ary relations (n > 1 an integer) on this set. Discussed are in particular the closure operators associated with certain n-ary relations on the digital line ℤ. Of these relations, we focus on a ternary one equipping the digital plane ℤ2 and the digital space ℤ3 with the closure operator associated with the direct product of two and three, respectively, copies of this ternary relation. The connectedness provided by the closure operator is shown to be suitable for defining digital curves satisfying a digital Jordan curve theorem and digital surfaces satisfying a digital Jordan surface theorem.

scholarly journals Reflective Full Subcategories of the Category ofL-Posets

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Hongping Liu ◽  
Qingguo Li ◽  
Xiangnan Zhou
Keyword(s):  
Special Class ◽  
Full Subcategory ◽  
Closure Operators ◽  
The Relationship ◽  
Equivalent Description

This paper focuses on the relationship betweenL-posets and completeL-lattices from the categorical view. By considering a special class of fuzzy closure operators, we prove that the category of completeL-lattices is a reflective full subcategory of the category ofL-posets with appropriate morphisms. Moreover, we characterize the Dedekind-MacNeille completions ofL-posets and provide an equivalent description for them.

scholarly journals The duality between the anti-exchange closure operators and the path independent choice operators on a finite set

2001 ◽  
Vol 41 (2) ◽  
pp. 131-150 ◽  
Author(s):  
Bernard Monjardet ◽  
Vololonirina Raderanirina
Keyword(s):  
Closure Operators ◽  
Finite Set

On Closure Operators, the Reals, and Choice

2004 ◽  
Vol 27 (2) ◽  
pp. 147-151
Author(s):  
Eraldo Giuli ◽  
Horst Herrlich
Keyword(s):  
Closure Operators

U-Closure Operators and Compactness

2005 ◽  
Vol 13 (5-6) ◽  
pp. 453-467 ◽  
Author(s):  
G. Castellini ◽  
E. Giuli
Keyword(s):  
Closure Operators

n-closure systems and n-closure operators

2006 ◽  
Vol 55 (2-3) ◽  
pp. 369-386 ◽  
Author(s):  
George Voutsadakis
Keyword(s):  
Closure Operators ◽  
Closure Systems

t-closure Operators

2018 ◽  
Vol 48 (2) ◽  
pp. 139-156 ◽  
Author(s):  
Mehmet Akif İnce ◽  
Funda Karaçal
Keyword(s):  
Closure Operators

scholarly journals Dual closure operators and their applications

2015 ◽  
Vol 439 ◽  
pp. 373-416 ◽  
Author(s):  
Dikran Dikranjan ◽  
Walter Tholen
Keyword(s):  
Closure Operators ◽  
Dual Closure

scholarly journals Small-scale characteristics of extremely high latitude aurora

2009 ◽  
Vol 27 (9) ◽  
pp. 3335-3347 ◽  
Author(s):  
J. A. Cumnock ◽  
L. G. Blomberg ◽  
A. Kullen ◽  
T. Karlsson ◽  
Keyword(s):  
High Latitude ◽  
Large Scale ◽  
Small Scale ◽  
Strong Correlations ◽  
Polar Cap ◽  
Plasma Flows ◽  
Ionospheric Convection ◽  
Local Closure ◽  
Scale Characteristics

Abstract. We examine 14 cases of an interesting type of extremely high latitude aurora as identified in the precipitating particles measured by the DMSP F13 satellite. In particular we investigate structures within large-scale arcs for which the particle signatures are made up of a group of multiple distinct thin arcs. These cases are chosen without regard to IMF orientation and are part of a group of 87 events where DMSP F13 SSJ/4 measures emissions which occur near the noon-midnight meridian and are spatially separated from both the dawnside and duskside auroral ovals by wide regions with precipitating particles typical of the polar cap. For 73 of these events the high-latitude aurora consists of a continuous region of precipitating particles. We focus on the remaining 14 of these events where the particle signatures show multiple distinct thin arcs. These events occur during northward or weakly southward IMF conditions and follow a change in IMF By. Correlations are seen between the field-aligned currents and plasma flows associated with the arcs, implying local closure of the FACs. Strong correlations are seen only in the sunlit hemisphere. The convection associated with the multiple thin arcs is localized and has little influence on the large-scale convection. This also implies that the sunward flow along the arcs is unrelated to the overall ionospheric convection.

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