⋆-closure Operators on Čech Closure Space

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.

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Some Variants of Normal Čech Closure Spaces via Canonically Closed Sets

Mathematics ◽

10.3390/math9111225 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1225

Author(s):

Ria Gupta ◽

Ananga Kumar Das

Keyword(s):

Closure Space ◽

Closed Sets ◽

Closure Spaces

New generalizations of normality in Čech closure space such as π-normal, weakly π-normal and κ-normal are introduced and studied using canonically closed sets. It is observed that the class of κ-normal spaces contains both the classes of weakly π-normal and almost normal Čech closure spaces.

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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.

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