Remark on Generalized Universal Covering Space in Digital Covering Theory

Han, Sang Eon

doi:10.5831/hmj.2009.31.3.267

Cited by 6 publications

(19 citation statements)

References 21 publications

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“…(2) As discussed by Han (2009c) (for more details, see another work of Han (2010d)), for the (k 0 , k 1 )-covering of Definition 4 we can replace "(k 0 , k 1 )-continuous surjection" with "surjection". Definition 7.…”

Section: Remarkmentioning

confidence: 99%

“…As a special case of this (k 1 , k 2 )-covering homomorphism, we obtain the digital version of Deck's transformation group of a covering map in algebraic topology (Spanier, 1966). Furthermore, by using the generalized universal covering property of Han (2009c), we can classify digital covering spaces.…”

Section: Remarkmentioning

confidence: 99%

“…Useful tools from algebraic topology and geometric topology for studying digital topological properties of a (binary) digital space include a digital covering space, a (digital) k-fundamental group, a digital k-surface and so forth. These have been studied in numerous papers (Boxer, 1999;Boxer and Karaca, 2008;Han, 2005b;2005c;2005d;2006a;2006b;2006c;2006d;2007a;2007b;2008a;2008b;2008c;2008d;2009a;2009b;2009c;2010a;2010b;2010c;Malgouyres and Lenoir, 2000;Khalimsky, 1987;Rosenfeld and Klette, 2003).…”

Section: Introductionmentioning

confidence: 99%

“…It is well known that for a covering (X, p, X), if the classical fundamental group π 1 (X) is an abelian group, then the total spaceX is regular (Massey, 1977;Spanier, 1966). Unlike these properties, their digital versions have some intrinsic features (Han, 2006b;2007b;2009a;2009b;2009c;2010a;2010b;2010c;In-Soo Kim and Han, 2008). Boxer and Karaca (2008) as well as Han (2006b;2007b;2008a;2008b;2009b) studied an automorphism group of a radius 2 (digital) covering (E, p, B).…”

Section: Introductionmentioning

confidence: 99%

“…In addition, Boxer and Karaca (2008) studied a classification of digital spaces by using the conjugacy class corresponding to a digital covering. Furthermore, Han (2009c) developed the generalized universal (briefly, GU-)covering property which improves the universal (2, k)-covering property of Boxer (2006).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Ultra regular covering space and its automorphism group

Han¹

2010

International Journal of Applied Mathematics and Computer Science

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In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces satisfying a radius 2 local isomorphism (Boxer and Karaca, 2008;Han, 2006b;2008b;2008d;2009b). However, for a digital covering which does not satisfy a radius 2 local isomorphism, the study of a digital fundamental group of a digital space and its automorphism group remains open. In order to examine this problem, the present paper establishes the notion of an ultra regular covering space, studies its various properties and calculates an automorphism group of the ultra regular covering space. In particular, the paper develops the notion of compatible adjacency of a digital wedge. By comparing an ultra regular covering space with a regular covering space, we can propose strong merits of the former.

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Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Ultra regular covering space and its automorphism group

Han¹

2010

International Journal of Applied Mathematics and Computer Science

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Equivalent conditions for digital covering maps

Pakdaman

Zakki

2020

Filomat

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It is known that every digital covering map p:(E,k) ? (B,?) has the unique path lifting property. In this paper, we show that its inverse is true when the continuous surjective map p has no conciliator point. Also, we prove that a digital (k,?)-continuous surjection p:(E,k)? (B,?) is a digital covering map if and only if it is a local isomorphism, when all digital spaces are connected. Moreover, we find out a loop criterion for a digital covering map to be a radius n covering map.

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