| Title:
|
Some cohomological aspects of the Banach fixed point principle (English) |
| Author:
|
Janoš, Ludvík |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
333-336 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $T\colon X\to X$ 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 $f=g-g\circ T$. (English) |
| Keyword:
|
Banach contraction |
| Keyword:
|
cohomology |
| Keyword:
|
cocycle |
| Keyword:
|
coboundary |
| Keyword:
|
separating family |
| Keyword:
|
core |
| MSC:
|
54H20 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1249.54081 |
| idMR:
|
MR2893980 |
| DOI:
|
10.21136/MB.2011.141653 |
| . |
| Date available:
|
2011-09-22T15:02:51Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141653 |
| . |
| Reference:
|
[1] Bakakhanian, A.: Cohomological Methods in Group Theory.Marcel Dekker, New York (1972). |
| Reference:
|
[2] Janoš, L.: The Banach contraction mapping principle and cohomology.Comment. Math. Univ. Carolin. 41 (2000), 605-610. MR 1795089 |
| . |
