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Fixed point property for digital spaces. (English) Zbl 1412.55007

Summary: The paper compares the fixed point property (FPP for short) of a compact Euclidean plane with its digital versions associated with Khalimsky and Marcus-Wyse topology. More precisely, by using a Khalimsky and a Marcus-Wyse topological digitization, the paper studies digital versions of the FPP for Euclidean topological spaces. Besides, motivated by the digital homotopy fixed point property (DHFP for brevity) [O. Ege and I. Karaca, C. R., Math., Acad. Sci. Paris 353, No. 11, 1029–1033 (2015; Zbl 06548156)], the present paper establishes the digital homotopy almost fixed point property (DHAFP for short) which is more generalized than the DHFP. Moreover, the present paper corrects some errors in [loc. cit.] and improves it.

MSC:

55N35 Other homology theories in algebraic topology
55M20 Fixed points and coincidences in algebraic topology
68R10 Graph theory (including graph drawing) in computer science
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)

Citations:

Zbl 06548156
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Full Text: DOI

References:

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