Exactly k-to-1 maps: from pathological functions with finitely many discontinuities to well-behaved covering maps

Details Exactly k-to-1 maps: from pathological functions with finitely many discontinuities to well-behaved covering maps Exactly k-to-1 maps: from pathological functions with finitely many discontinuities to well-behaved covering maps

1998-10-20

arxiv.org/abs/math/9810129v1

Continua with the Houston Problem Book, Lecture Notes in Pure and Applied Mathematics, Series/170, Marcel Dekker, New York, 19

Mathematics

General Topology

14 pages

Scientific paper

Many mathematicians encounter k-to-1 maps only in the study of covering maps. But, of course, k-to-1 maps do not have to be open. This paper touches on covering maps, and simple maps, but concentrates on ordinary k-to-1 functions (both continuous and finitely discontinuous) from one metric continuum to another. New results, old results and ideas for further research are given; and a baker's dozen of questions are raised.

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