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J. Korean Math. Soc. 2017; 54(4): 1231-1242
Online first article May 29, 2017 Printed July 1, 2017
https://doi.org/10.4134/JKMS.j160434
Copyright © The Korean Mathematical Society.
Factorization of certain self-maps of product spaces
Sangwoo Jun and Kee Young Lee
Korea University, Korea University
In this paper, we show that, under some conditions, self-maps of product spaces can be represented by the composition of two specific self-maps if their induced homomorphism on the $i$-th homotopy group is an automorphism for all $i$ in some section of positive integers. As an application, we obtain closeness numbers of several product spaces.
Keywords: reducible, $k$-reducible, self-homotopy equivalence, self-closeness number
MSC numbers: Primary 55Q05; Secondary 55P10
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