Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2021; 58(2): 445-449

Online first article February 24, 2021      Printed March 31, 2021

https://doi.org/10.4134/BKMS.b200352

Copyright © The Korean Mathematical Society.

Relative self-closeness numbers

Toshihiro Yamaguchi

Kochi University

Abstract

We define the relative self-closeness number $N{\mathcal E}(g)$ of a map $g:X\overset{}{\to} Y$, which is a generalization of the self-closeness number $N{\mathcal E}(X)$ of a connected CW complex $X$ defined by Choi and Lee \cite{ChoiLee15}. Then we compare $N{\mathcal E}(p)$ with $N{\mathcal E}(X)$ for a fibration $X\to E\overset{p}{\to} Y$. Furthermore we obtain its rationalized result.

Keywords: Self-homotopy equivalence, fibration, relative self-closeness number, Sullivan model

MSC numbers: 55P10, 55P62, 55Q05, 55R05

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