Relative self-closeness numbers
Bull. Korean Math. Soc. 2021 Vol. 58, No. 2, 445-449
Published online February 24, 2021
Printed March 31, 2021
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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