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http://dx.doi.org/10.5831/HMJ.2013.35.4.707

STUDY ON TOPOLOGICAL SPACES WITH THE SEMI-T½ SEPARATION AXIOM  

Han, Sang-Eon (Faculty of Liberal Education, Institute of Pure and Applied Mathematics, Chonbuk National University)
Publication Information
Honam Mathematical Journal / v.35, no.4, 2013 , pp. 707-716 More about this Journal
Abstract
The present paper consists of two parts. Since the recent paper [4] proved that an Alexandroff $T_0$-space is a semi-$T_{\frac{1}{2}}$-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 ($SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$, k) relative to the simple closed $k_i$-curves $SC^{n_i,l_i}_{k_i}$, $i{\in}\{1,2\}$ 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-$T_{\frac{1}{2}}$-separation axiom; semi-open; semi-closed; upper set; normal adjacency; digital product; digital covering space;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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