# Strong homotopy of digitally continuous functions

@article{Staecker2019StrongHO, title={Strong homotopy of digitally continuous functions}, author={P. C. Staecker}, journal={ArXiv}, year={2019}, volume={abs/1903.00706} }

We introduce a new type of homotopy relation for digitally continuous functions which we call ``strong homotopy.'' Both digital homotopy and strong homotopy are natural digitizations of classical topological homotopy: the difference between them is analogous to the difference between digital 4-adjacency and 8-adjacency in the plane.
We explore basic properties of strong homotopy, and give some equivalent characterizations. In particular we show that strong homotopy is related to ``punctuated… Expand

#### 4 Citations

Strong homotopy in finite topological adjacency category

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Abstract The present paper investigates a strong homotopy (i.e., SA-homotopy) in a finite topological adjacency category. We prove that two minimal finite spaces are SA-homotopy equivalent if and… Expand

The two digital homology theories

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In this paper we prove results relating to four homology theories developed in the topology of digital images: a simplicial homology theory by Arslan et al which is the homology of the clique… Expand

A fundamental group for digital images

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A functor from digital images to groups, which closely resembles the ordinary fundamental group from algebraic topology, is constructed, which shows that the fundamental group is preserved by subdivision. Expand

Hyperspaces and Function Graphs in Digital Topology

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We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and… Expand

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