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

Colloquium Mathematicae (1993)

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

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topKato, 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] K. Borsuk, Theory of Retracts, Monografie Mat. 44, PWN, Warszawa, 1967. Zbl0153.52905
- [2] H. Cook, Continua which admit only the identity mapping onto non-degenerate subcontinua, Fund. Math. 60 (1967), 241-249. Zbl0158.41503
- [3] S. Kinoshita, On essential components of the set of fixed points, Osaka J. Math. 4 (1952), 19-22. Zbl0047.16204
- [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