1. CMB 2011 (vol 55 pp. 523)
 Iwase, Norio; Mimura, Mamoru; Oda, Nobuyuki; Yoon, Yeon Soo

The MilnorStasheff Filtration on Spaces and Generalized Cyclic Maps
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.
Keywords:Gottlieb sets for maps, LS category, Tspaces Categories:55P45, 55P35 
