The digital smash product

Ismet Cinar; Ozgur Ege; Ismet Karaca; Ismet Cinar; Ozgur Ege; Ismet Karaca

doi:10.3934/era.2020026

Electronic Research Archive

2020, Volume 28, Issue 1: 459-469. doi: 10.3934/era.2020026

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The digital smash product

Department of Mathematics, Ege University, Bornova, 35100, Izmir, Turkey

Received: 01 November 2019
Primary: 46M20; Secondary: 68U05, 68U10

In this paper, we construct the smash product from the digital viewpoint and prove some its properties such as associativity, distributivity, and commutativity. Moreover, we present the digital suspension and the digital cone for an arbitrary digital image and give some examples of these new concepts.
- Digital image,
- digital smash product,
- digital shy map,
- digital suspension,
- digital cone
Citation: Ismet Cinar, Ozgur Ege, Ismet Karaca. The digital smash product[J]. Electronic Research Archive, 2020, 28(1): 459-469. doi: 10.3934/era.2020026

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Abstract

In this paper, we construct the smash product from the digital viewpoint and prove some its properties such as associativity, distributivity, and commutativity. Moreover, we present the digital suspension and the digital cone for an arbitrary digital image and give some examples of these new concepts.

References

[1]	Digitally continuous functions. Pattern Recogn. Lett. (1994) 15: 833-839.
[2]	A classical construction for the digital fundamental group. J. Math. Imaging Vis. (1999) 10: 51-62.
[3]	Properties of digital homotopy. J. Math. Imaging Vis. (2005) 22: 19-26.
[4]	Digital products, wedges and covering spaces. J. Math. Imaging Vis. (2006) 25: 159-171.
[5]	Digital shy maps. Appl. Gen. Topol. (2017) 18: 143-152.
[6]	Fundamental groups for digital products. Adv. Appl. Math. Sci. (2012) 11: 161-179.
[7]	Topological invariants in digital images. J. Math. Sci. Adv. Appl. (2011) 11: 109-140.
[8]	Some new results on connected sum of certain digital surfaces. Malaya J. Matematik (2019) 7: 318-325.
[9]	Fundamental properties of simplicial homology groups for digital images. Amer. J. Comput. Tech. Appl. (2013) 1: 25-42.
[10]	Cohomology theory for digital images. Rom. J. Inf. Sci. Tech. (2013) 16: 10-28.
[11]	Digital cohomology operations. Appl. Math. Inform. Sci. (2015) 9: 1953-1960.
[12]	Digital fibrations. Proc. Natl. Acad. Sci. India Sect. A Phys. Sci. (2017) 87: 109-114.
[13]	Relative homology groups of digital images. Appl. Math. Inform. Sci. (2014) 8: 2337-2345.
[14]	Oriented surfaces in digital spaces. CVGIP. Graph Model Im. Proc. (1993) 55: 381-396.
[15]	The cohomology structure of digital Khalimsky spaces. Rom. J. Math. Comput. Sci. (2018) 8: 110-128.
[16]	Some results on simplicial homology groups of 2D digital images. Int. J. Inform. Comput. Sci. (2012) 1: 198-203.
[17]	A topological approach to digital topology. Amer. Math. Monthly (1991) 98: 901-917.
[18]	Digital topology, introduction and survey. Comput. Vision Graphics Image Process. (1989) 48: 357-393.
[19]	A Jordan surface theorem for three dimensional digital spaces. Discrete Comput. Geom. (1991) 6: 155-161.
[20]	Finite topology as applied to image analysis. Comput. Vision Graphics Image Process. (1989) 46: 141-161.
[21]	Digital topology. Amer. Math. Monthly (1979) 86: 621-630.
[22]	Continuous functions on digital pictures. Pattern Recogn. Lett. (1986) 4: 177-184.

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