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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 $Z^{n_i}$, $i{\in}\{1,2\}$ denoted by $SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$. Since a normal adjacency for this product and the $L_C$-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 $L_C$-property? This research plays an important role in studying product properties of digital topological properties.
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참고문헌 (31)
참고문헌 신청
C. Berge / 1976 / Graphs and Hypergraphs / North-Holland
G. Bertrand / 1994 / Simple points, topological numbers and geodesic neighborhoods in cubic grids / Pattern Recognition Letters 15:1003~1011
G. Bertrand / 1999 / Some topological properties of discrete surfaces / Jour. of Mathematical Imaging and Vision 20:207~221
L. Boxer / 1999 / A classical construction for the digital fundamental group / Jour. of Mathematical Imaging and Vision 10:51~62
L. Chen / 2004 / Discrete Surfaces and Manifolds: A Theory of Digital Discrete Geom-etry and Topology / Scientific and Practical Computing
G. Bertrand / 1994 / Simple points, topological numbers and geodesic neighborhoods in cubic grids / Pattern Recognition Letters 15:1003~1011
G. Bertrand / 1999 / Some topological properties of discrete surfaces / Jour. of Mathematical Imaging and Vision 20:207~221
L. Boxer / 1999 / A classical construction for the digital fundamental group / Jour. of Mathematical Imaging and Vision 10:51~62
L. Chen / 2004 / Discrete Surfaces and Manifolds: A Theory of Digital Discrete Geom-etry and Topology / Scientific and Practical Computing
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