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(a) Show that the eight-point set surrounding an open point in the digital plane is a digital simple closed curve. (b) Show that the eight-point set surrounding a closed point in the digital plane is a digital simple closed curve. (c) Show that the eight-point set surrounding a mixed point in the digital plane is not a digital simple closed curve. Does such a set separate the digital plane?

(a) Show that the eight-point set surrounding an open point in the digital plane is a digital simple closed curve. (b) Show that the eight-point set surrounding a closed point in the digital plane is a digital simple closed curve. (c) Show that the eight-point set surrounding a mixed point in the digital plane is not a digital simple closed curve. Does such a set separate the digital plane?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Show that the eight-point set surrounding an open point in the digital plane is a digital simple closed curve. (b) Show that the eight-point set surrounding a closed point in the digital plane is a digital simple closed curve. (c) Show that the eight-point set surrounding a mixed point in the digital plane is not a digital simple closed curve. Does such a set separate the digital plane?
Transcribed Image Text:(a) Show that the eight-point set surrounding an open point in the digital plane is a digital simple closed curve. (b) Show that the eight-point set surrounding a closed point in the digital plane is a digital simple closed curve. (c) Show that the eight-point set surrounding a mixed point in the digital plane is not a digital simple closed curve. Does such a set separate the digital plane?
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