scholarly journals Closure Operators in Convergence Approach Spaces

2021 ◽  
Keyword(s):  
Closure Operators ◽  
Convergence Approach Spaces ◽  
Approach Spaces

Convergence Approach Spaces : Actions

2015 ◽  
Vol 24 (2) ◽  
pp. 147-161 ◽  
Author(s):  
E. Colebunders ◽  
H. Boustique ◽  
P. Mikusiński ◽  
G. Richardson
Keyword(s):  
Convergence Approach Spaces ◽  
Approach Spaces

scholarly journals On the continuous action of enriched lattice-valued convergence groups: Some examples

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3045-3064
Author(s):  
T.M.G. Ahsanullah ◽  
Fawzi Al-Thukair ◽  
Jawaher Al-Mufarrij
Keyword(s):  
Transformation Group ◽  
Transformation Groups ◽  
Triangular Norm ◽  
Topological Transformation ◽  
Continuous Action ◽  
Convergence Spaces ◽  
Group A ◽  
Convergence Approach Spaces ◽  
Cartesian Closed ◽  
Approach Spaces

Starting with a category SL-CONVGRP, of stratified enriched cl-premonoid-valued convergence groups as introduced earlier, we present a category SL-CONVTGRP, of stratified enriched cl-premonoid-valued convergence transformation groups, the idea behind this category is crept in the notion of convergence transformation group - a generalization of topological transformation group. In this respect, we are able to provide natural examples in support to our endeavor; these examples, however, stem from the action of convergence approach groups on convergence approach spaces, and the action of probabilistic convergence groups under triangular norm on probabilistic convergence spaces. Based on the category of enriched lattice-valued convergence spaces, a Cartesian closed category that enjoys lattice-valued convergence structure on function space, we look into among others, the lattice-valued convergence structures on the group of homeomorphisms of enriched lattice-valued convergence spaces, generalizing a concept of convergence transformation groups on convergence spaces, obtaining a characterization.

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.

On Closure Operators, the Reals, and Choice

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