Rad HAZU, Matematičke znanosti, Vol. 27 (2023), 245-257.

THE HUREWICZ THEOREM IN Sho* AND Sho*2

Nikola Koceić Bilan and Ivančica Mirošević

Faculty of Science, University of Split, 21 000 Split, Croatia
e-mail: koceic@pmfst.hr

Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, 21 000 Split, Croatia
e-mail: ivancica.mirosevic@fesb.hr

Abstract.   The Hurewicz isomorphism theorem relating coarse shape groups and coarse shape homology groups of pointed metric continua is proved. A similar statement is proposed and proved in the category Sho*2 for relative coarse shape pro-groups and coarse shape homology pro-groups, and consequently a relative variant for relative coarse shape groups and coarse shape homology groups of pointed pairs of metric continua is given.

2020 Mathematics Subject Classification.   55P55, 55Q05, 55N99.

Key words and phrases.   Coarse shape group, Hurewicz theorem, homotopy, homology.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/ypn4ocdn79

References:

  1. N. Koceić Bilan, The induced homology and homotopy functors on the coarse shape category, Glas. Mat. Ser. III 45(65) (2010), 531-557.
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  2. N. Koceić Bilan, The coarse shape groups, Topology Appl. 157 (2010), 894-901.
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  3. N. Koceić Bilan, Continuity of coarse shape groups, Homology Homotopy Appl. 18 (2016), 209-215,
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  4. N. Koceić Bilan and I. Mirošević, Functorial reducing pro*-Grp category to pro-Grp, Topology Appl. 263 (2019), 74-89.
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