U-Closure Operators and Compactness

G. Castellini; E. Giuli

doi:10.1007/s10485-005-9001-8

U-Closure Operators and Compactness

Applied Categorical Structures ◽

10.1007/s10485-005-9001-8 ◽

2005 ◽

Vol 13 (5-6) ◽

pp. 453-467 ◽

Cited By ~ 3

Author(s):

G. Castellini ◽

E. Giuli

Keyword(s):

Closure Operators

Download Full-text

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

Fundamenta Informaticae ◽

10.3233/fi-2021-2013 ◽

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.

Download Full-text

Reflective Full Subcategories of the Category ofL-Posets

Abstract and Applied Analysis ◽

10.1155/2012/891239 ◽

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.

Download Full-text