Covering maps that are not compositions of covering maps of lesser order
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Abstract:
In 1995 J.W. Heath asked which exactly $n$-to-one maps are compositions of exactly $k$-to-one maps with $1<k<n$. This paper deals with compositions of covering maps. Exactly $n$-to-one covering maps on locally arcwise connected continua that are not factorable into covering maps of order $\leq n-1$ are constructed for all $n$’s, and characterized in algebraic terms (fundamental groups). They are not proper compositions of exactly $k$-to-one maps, open maps, or locally one-to-one maps.References
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Additional Information
- Jerzy Krzempek
- Affiliation: Institute of Mathematics, Silesian Technical University, Kaszubska 23, PL-44-100 Gliwice, Poland
- Email: krzem@zeus.polsl.gliwice.pl
- Received by editor(s): November 6, 2000
- Received by editor(s) in revised form: January 9, 2001
- Published electronically: November 15, 2001
- Communicated by: Alan Dow
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1867-1873
- MSC (2000): Primary 54C10; Secondary 05C25
- DOI: https://doi.org/10.1090/S0002-9939-01-06266-9
- MathSciNet review: 1887036