A note on f.p.p. and $f^*.p.p.$

• Autorzy: Hisao Kato
• Języki publikacji: EN

Abstrakty

EN

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 $f^*.p.p.$

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 66
• Numer: 1
• Strony: 147-150

Daty

wydano

1993

otrzymano

1992-11-23

poprawiono

1993-03-15

Twórcy

autor

Hisao Kato

• Faculty of Integrated Arts and Sciences, Hiroshima University, 1-7-1 Kagamiyama, Higasi-Hiroshima 724, Japan

Bibliografia

• [1] K. Borsuk, Theory of Retracts, Monografie Mat. 44, PWN, Warszawa, 1967.
• [2] H. Cook, Continua which admit only the identity mapping onto non-degenerate subcontinua, Fund. Math. 60 (1967), 241-249.
• [3] S. Kinoshita, On essential components of the set of fixed points, Osaka J. Math. 4 (1952), 19-22.
• [4] Y. Yonezawa, On f.p.p. and $f^*.p.p.$ of some not locally connected continua, Fund. Math. 139 (1991), 91-98.