# A note on f.p.p. and ${f}^{*}.p.p.$

Colloquium Mathematicae (1993)

• Volume: 66, Issue: 1, page 147-150
• ISSN: 0010-1354

top

## Abstract

top
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 ${f}^{*}.p.p.$

## How to cite

top

Kato, Hisao. "A note on f.p.p. and $f^*.p.p.$." Colloquium Mathematicae 66.1 (1993): 147-150. <http://eudml.org/doc/210227>.

@article{Kato1993,
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 $f^*.p.p.$},
author = {Kato, Hisao},
journal = {Colloquium Mathematicae},
language = {eng},
number = {1},
pages = {147-150},
title = {A note on f.p.p. and $f^*.p.p.$},
url = {http://eudml.org/doc/210227},
volume = {66},
year = {1993},
}

TY - JOUR
AU - Kato, Hisao
TI - A note on f.p.p. and $f^*.p.p.$
JO - Colloquium Mathematicae
PY - 1993
VL - 66
IS - 1
SP - 147
EP - 150
AB - 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 $f^*.p.p.$
LA - eng
UR - http://eudml.org/doc/210227
ER -

## References

top
1. [1] K. Borsuk, Theory of Retracts, Monografie Mat. 44, PWN, Warszawa, 1967. Zbl0153.52905
2. [2] H. Cook, Continua which admit only the identity mapping onto non-degenerate subcontinua, Fund. Math. 60 (1967), 241-249. Zbl0158.41503
3. [3] S. Kinoshita, On essential components of the set of fixed points, Osaka J. Math. 4 (1952), 19-22. Zbl0047.16204
4. [4] Y. Yonezawa, On f.p.p. and ${f}^{*}.p.p.$ of some not locally connected continua, Fund. Math. 139 (1991), 91-98. Zbl0754.54031

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.