Structuring Digital Spaces by Path-Partition Induced Closure Operators on Graphs

2017 ◽  
pp. 43-55
Author(s):  
Josef Šlapal
Keyword(s):  
Closure Operators ◽  
Path Partition ◽  
Digital Spaces

Graphs with a path partition for structuring digital spaces

2013 ◽  
Vol 233 ◽  
pp. 305-312 ◽  
Author(s):  
Josef Šlapal
Keyword(s):  
Path Partition ◽  
Digital Spaces

scholarly journals Closure operators on graphs for modeling connectedness in digital spaces

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5011-5021 ◽  
Author(s):  
Josef Slapal
Keyword(s):  
Jordan Curve ◽  
Jordan Curve Theorem ◽  
Digital Form ◽  
Closure Operators ◽  
Adjacency Graph ◽  
Simple Graphs ◽  
Basic Properties ◽  
Vertex Sets ◽  
Khalimsky Topology ◽  
Digital Spaces

For undirected simple graphs, we introduce closure operators on their vertex sets induced by sets of walks of the same lengths. Some basic properties of these closure operators are studied, with greater attention paid to connectedness. We focus on the closure operators induced by certain sets of walks in the 2-adjacency graph on the digital line Z, which generalize the Khalimsky topology. For the closure operators on Z2 obtained as particularly defined products of pairs of the induced closure operators on Z, we formulate and prove a digital form of the Jordan curve theorem.

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
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