STUDY ON TOPOLOGICAL SPACES WITH THE SEMI-T½ SEPARATION AXIOM

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 4,  2013, pp.707-716
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.4.707
Title & Authors
STUDY ON TOPOLOGICAL SPACES WITH THE SEMI-T½ SEPARATION AXIOM
Han, Sang-Eon;

Abstract
The present paper consists of two parts. Since the recent paper [4] proved that an Alexandroff $\small{T_0}$-space is a semi-$\small{T_{\frac{1}{2}}}$-space, the first part studies semi-open and semi-closed structures of the Khalimsky nD space. The second one focuses on the study of a relation between the LS-property of ($\small{SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}}$, k) relative to the simple closed $\small{k_i}$-curves $\small{SC^{n_i,l_i}_{k_i}}$, $\small{i{\in}\{1,2\}}$ and its normal k-adjacency. In addition, the present paper points out that the main theorems of Boxer and Karaca's paper [3] such as Theorems 4.4 and 4.7 of [3] cannot be new assertions. Indeed, instead they should be attributed to Theorems 4.3 and 4.5, and Example 4.6 of [10].
Keywords
digital topology;domain theory;semi-$\small{T_{\frac{1}{2}}}$-separation axiom;semi-open;semi-closed;upper set;normal adjacency;digital product;digital covering space;
Language
English
Cited by
1.
UTILITY OF DIGITAL COVERING THEORY,;;

호남수학학술지, 2014. vol.36. 3, pp.695-706
2.
COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT,;

호남수학학술지, 2015. vol.37. 1, pp.135-147
3.
REMARKS ON HOMOTOPIES ASSOCIATED WITH KHALIMSKY TOPOLOGY,;;

호남수학학술지, 2015. vol.37. 4, pp.577-593
1.
COMPARISON AMONG SEVERAL ADJACENCY PROPERTIES FOR A DIGITAL PRODUCT, Honam Mathematical Journal, 2015, 37, 1, 135
2.
REMARKS ON HOMOTOPIES ASSOCIATED WITH KHALIMSKY TOPOLOGY, Honam Mathematical Journal, 2015, 37, 4, 577
3.
UTILITY OF DIGITAL COVERING THEORY, Honam Mathematical Journal, 2014, 36, 3, 695
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