Abstract view
The MilnorStasheff Filtration on Spaces and Generalized Cyclic Maps


Published:20110629
Printed: Sep 2012
Norio Iwase,
Faculty of Mathematics, Kyushu University, Fukuoka 8190395, Japan
Mamoru Mimura,
Department of Mathematics, Okayama University, Okayama 7008530, Japan
Nobuyuki Oda,
Department of Applied Mathematics, Fukuoka University, Fukuoka 8140180, Japan
Yeon Soo Yoon,
Department of Mathematics Education, Hannam University, Daejeon 306791, Korea
Abstract
The concept of $C_{k}$spaces is introduced, situated at an
intermediate stage between $H$spaces and $T$spaces. The
$C_{k}$space corresponds to the $k$th MilnorStasheff filtration on
spaces. It is proved that a space $X$ is a $C_{k}$space if and only
if the Gottlieb set $G(Z,X)=[Z,X]$ for any space $Z$ with ${\rm cat}\,
Z\le k$, which generalizes the fact that $X$ is a $T$space if and
only if $G(\Sigma B,X)=[\Sigma B,X]$ for any space $B$. Some results
on the $C_{k}$space are generalized to the $C_{k}^{f}$space for a
map $f\colon A \to X$. Projective spaces, lens spaces and spaces with
a few cells are studied as examples of $C_{k}$spaces, and
non$C_{k}$spaces.