A note on f.p.p. and $f^*.p.p.$
Volume 66 / 1993
Colloquium Mathematicum 66 (1993), 147-150
DOI: 10.4064/cm-66-1-147-150
Abstract
In [3], Kinoshita defined the notion of $f^*.p.p.$ and he proved that each compact AR has $f^*.p.p.$ In [4], Yonezawa gave some examples of not locally connected continua with f.p.p., but without $f^*.p.p.$ In general, for each n=1,2,..., there is an n-dimensional continuum $X_n$ with f.p.p., but without $f^*.p.p.$ such that $X_n$ is locally (n-2)-connected (see [4, Addendum]). In this note, we show that for each n-dimensional continuum X which is locally (n-1)-connected, X has f.p.p. if and only if X has $f^*.p.p.$
