STUDY ON TOPOLOGICAL SPACES WITH THE SEMI-T<sub>½</sub>SEPARATION AXIOM

Han, Sang-Eon

doi:10.5831/hmj.2013.35.4.707

Cited by 11 publications

(9 citation statements)

References 12 publications

(38 reference statements)

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“…A topological space (X, T) is called an Alexandroff space if every point x ∈ X has the smallest open neighborhood in (X, T) [2]. Motivated by the Alexandroff topological structure [1,2], several kinds of digital topological spaces and locally finite spaces were developed such as an n-dimensional K-topological space [21], an M-topological space, an axiomatic locally finite space [24], a space set topological space [18] and so on [15,21,24,28]. Furthermore, a study of their properties is included in the papers [11, 20-22, 24, 29].…”

Section: Preliminariesmentioning

confidence: 99%

Hereditary properties of semi-separation axioms and their applications

Han¹

2018

Filomat

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The paper studies the open-hereditary property of semi-separation axioms and applies it to the study of digital topological spaces such as an n-dimensional Khalimsky topological space, a Marcus-Wyse topological space and so on. More precisely, we study various properties of digital topological spaces related to low-level and semi-separation axioms such as T 1 2 , semi-T 1 2 , semi-T 1 , semi-T 2 , etc. Besides, using the finite or the infinite product property of the semi-T i-separation axiom, i ∈ {1, 2}, we prove that the n-dimensional Khalimsky topological space is a semi-T 2-space. After showing that not every subspace of the digital topological spaces satisfies the semi-T i-separation axiom, i ∈ {1, 2}, we prove that the semi-T iseparation property is open-hereditary, i ∈ {1, 2}. All spaces in the paper are assumed to be nonempty and connected.

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Section: Preliminariesmentioning

confidence: 99%

Hereditary properties of semi-separation axioms and their applications

Han¹

2018

Filomat

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“…[3,5]. In relation to the digital adjacency of the product, several kinds of tools have been studied such as a normal adjacency [5], the properties L C [10] and L S [12] and their various properties [14,15,18]. Proof: To address the following query "In KDTC and CTC, what is the topological structure in the Cartesian product X × [0, m] Z ?…”

Section: Remarks On Homotopies In Kdtc and Ctcmentioning

confidence: 99%

Remarks on Homotopies Associated With Khalimsky Topology

Han¹,

Lee²

2015

Honam Mathematical Journal

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“…and the L S -property of this product with some k-adjacency (for more detail, see the papers [21,22,24]). …”

Section: Example 42 By Using the Simple Closed K-curves Inmentioning

confidence: 99%

“…Indeed, a digital image (X, k) can be considered to be a set X ⊂ Z n with a k-adjacency relation on Z n (or an adjacency graph), where Z n is the set of points in the Euclidean nD space with integer coordinates, n ∈ N and N is the set of natural numbers. To study digital topological properties of a digital image (X, k), we have used various tools such as a digital fundamental group [4,13,18], digital covering spaces [7,8,14,15,16,19,20], digital homotopy equivalences [6,17,26] and digital k-surface structures [2,3,5,10,21].…”

Section: Introductionmentioning

confidence: 99%

Comparison Among Several Adjacency Properties for a Digital Product

Han¹

2015

Honam Mathematical Journal

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Abstract. Owing to the notion of a normal adjacency for a digital product in [8], the study of product properties of digital topological properties has been substantially done. To explain a normal adjacency of a digital product more efficiently, the recent paper [22] proposed an S-compatible adjacency of a digital product. Using an S-compatible adjacency of a digital product, we also study product properties of digital topological properties, which improves the presentations of a normal adjacency of a digital product in [8]. Besides, the paper [16] studied the product property of two digital covering maps in terms of the L S -and the L C -property of a digital product which plays an important role in studying digital covering and digital homotopy theory. Further, by using HS-and HC-properties of digital products, the paper [18] studied multiplicative properties of a digital fundamental group. The present paper compares among several kinds of adjacency relations for digital products and proposes their own merits and further, deals with the problem: consider a Cartesian product of two simple closed k i -curves with l i elements in. Since a normal adjacency for this product and the LC -property are different from each other, the present paper address the problem: for the digital product does it have both a normal k-adjacency of Z n 1 +n 2 and another adjacency satisfying the LC -property? This research plays an important role in studying product properties of digital topological properties.

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STUDY ON TOPOLOGICAL SPACES WITH THE SEMI-T_½SEPARATION AXIOM

Cited by 11 publications

References 12 publications

Hereditary properties of semi-separation axioms and their applications

Hereditary properties of semi-separation axioms and their applications

Remarks on Homotopies Associated With Khalimsky Topology

Comparison Among Several Adjacency Properties for a Digital Product

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STUDY ON TOPOLOGICAL SPACES WITH THE SEMI-T½SEPARATION AXIOM

Cited by 11 publications

References 12 publications

Hereditary properties of semi-separation axioms and their applications

Hereditary properties of semi-separation axioms and their applications

Remarks on Homotopies Associated With Khalimsky Topology

Comparison Among Several Adjacency Properties for a Digital Product

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Product

Resources

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STUDY ON TOPOLOGICAL SPACES WITH THE SEMI-T_½SEPARATION AXIOM