Some cohomological aspects of the Banach fixed point principle

Janoš, Ludvík. "Some cohomological aspects of the Banach fixed point principle." Mathematica Bohemica 136.3 (2011): 333-336. <http://eudml.org/doc/197048>.

@article{Janoš2011,
abstract = {Let $T\colon X\rightarrow X$ be a continuous selfmap of a compact metrizable space $X$. We prove the equivalence of the following two statements: (1) The mapping $T$ is a Banach contraction relative to some compatible metric on $X$. (2) There is a countable point separating family $\mathcal \{F\}\subset \mathcal \{C\}(X)$ of non-negative functions $f\in \mathcal \{C\}(X)$ such that for every $f\in \mathcal \{F\}$ there is $g\in \mathcal \{C\}(X)$ with $f=g-g\circ T$.},
author = {Janoš, Ludvík},
journal = {Mathematica Bohemica},
keywords = {Banach contraction; cohomology; cocycle; coboundary; separating family; core; Banach contraction; cohomology; cocycle; coboundary; separating family; core},
language = {eng},
number = {3},
pages = {333-336},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some cohomological aspects of the Banach fixed point principle},
url = {http://eudml.org/doc/197048},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Janoš, Ludvík
TI - Some cohomological aspects of the Banach fixed point principle
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 3
SP - 333
EP - 336
AB - Let $T\colon X\rightarrow X$ be a continuous selfmap of a compact metrizable space $X$. We prove the equivalence of the following two statements: (1) The mapping $T$ is a Banach contraction relative to some compatible metric on $X$. (2) There is a countable point separating family $\mathcal {F}\subset \mathcal {C}(X)$ of non-negative functions $f\in \mathcal {C}(X)$ such that for every $f\in \mathcal {F}$ there is $g\in \mathcal {C}(X)$ with $f=g-g\circ T$.
LA - eng
KW - Banach contraction; cohomology; cocycle; coboundary; separating family; core; Banach contraction; cohomology; cocycle; coboundary; separating family; core
UR - http://eudml.org/doc/197048
ER -