Corpus ID: 67856473

Strong homotopy of digitally continuous functions

  title={Strong homotopy of digitally continuous functions},
  author={P. C. Staecker},
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
Strong homotopy in finite topological adjacency category
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A Classical Construction for the Digital Fundamental Group
  • L. Boxer
  • Mathematics, Computer Science
  • Journal of Mathematical Imaging and Vision
  • 2004
The digital fundamental group is constructed based on the notions of digitally continuous functions presented in [10] and digital homotopy and yields isomorphic fundamental groups for the digital images considered in the latter papers (for certain connectedness types). Expand
Fixed poin sets in digital topology, 1
In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topologicalExpand
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This paper develops a numerical digital homotopy invariant and begins to catalog all possible connected digital images on a small number of points, up to Homotopy equivalence. Expand
Properties of Digital Homotopy
  • L. Boxer
  • Mathematics, Computer Science
  • Journal of Mathematical Imaging and Vision
  • 2005
A variety of digitally-continuous functions that preserve homotopy types or homotopic-related properties such as the digital fundamental group are studied. Expand
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