Abstract
In the previous chapter we have pointed out the existence of digital spaces (V,π) for which π,π is a strong Jordan pair. According to Theorem 6.4.1, all 1-simply connected digital spaces are in this category, including by Theorem 6.4.5 (ZN , α N ), (ZN ,δ N ), (ZN , κ N ), (ZN , ε e ) (for any N-dimensional direction vector e) and, when N ≥ 2, (ZN , β s ), for any N-dimensional sign function s. That the digital spaces of this last kind have the stated property also follows directly from Theorem 6.3.13. We have also shown (in Theorem 6.3.14) that the fcc grid with face-adjacency (i.e., (F, β 1 )) also has the stated property. Following [2], we refer to digital spaces with this property as strong Jordan graphs.
“And stretch de boundary line to de oder side ob Jordan.”
Jordan is a Hard Road to Travel, a song by D. D. Emmett.
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© 1998 Birkhäuser Boston
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Herman, G.T. (1998). Jordan Graphs. In: Geometry of Digital Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4136-2_7
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DOI: https://doi.org/10.1007/978-1-4612-4136-2_7
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8669-1
Online ISBN: 978-1-4612-4136-2
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