| Title:
|
On linear functorial operators extending pseudometrics (English) |
| Author:
|
Banakh, T. |
| Author:
|
Pikhurko, O. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
343-348 |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a functor $F\supset Id$ on the category of metrizable compacta, we introduce a conception of a linear functorial operator $T=\{T_X:Pc(X)\to Pc(FX)\}$ extending (for each $X$) pseudometrics from $X$ onto $FX\supset X$ (briefly LFOEP for $F$). The main result states that the functor $SP^n_G$ of $G$-symmetric power admits a LFOEP if and only if the action of $G$ on $\{1,\dots,n\}$ has a one-point orbit. Since both the hyperspace functor $\exp$ and the probability measure functor $P$ contain $SP^2$ as a subfunctor, this implies that both $\exp$ and $P$ do not admit LFOEP. (English) |
| Keyword:
|
linear functorial operator extending (pseudo)metrics |
| Keyword:
|
the functor of $G$-symmetric power |
| MSC:
|
46M15 |
| MSC:
|
54B30 |
| MSC:
|
54C20 |
| MSC:
|
54E35 |
| idZBL:
|
Zbl 0886.54010 |
| idMR:
|
MR1455501 |
| . |
| Date available:
|
2009-01-08T18:31:20Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118932 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/118975 |
| . |
| Reference:
|
Banakh T.: AE(0)-spaces and regular operators extending (averaging) pseudometrics.Bull. Polon. Acad. Sci. Ser. Sci. Math. (1994), 42 197-206. Zbl 0827.54010, MR 1811849 |
| Reference:
|
Bessaga C., Pełczyński A.: On the spaces of measurable functions.Studia Math. 44 (1972), 597-615. MR 0368068 |
| Reference:
|
Fedorchuk V.V.: On some geometric properties of covariant functors (in Russian).Uspekhi Mat. Nauk 39 (1984), 169-208. MR 0764014 |
| Reference:
|
Fedorchuk V.V.: Triples of infinite iterates of metrizable functors (in Russian).Izv. Akad. Nauk SSSR Ser. Mat. (1990), 54 396-418. |
| Reference:
|
Fedorchuk V.V., Filippov V.V.: General Topology. Principal Constructions (in Russian).Moscow Univ. Press Moscow (1988). |
| Reference:
|
Pikhurko O.: Extending metrics in compact pairs.Mat. Studiï 3 (1994), 103-106. Zbl 0927.54029, MR 1692801 |
| Reference:
|
Zarichnyi M.: Regular linear operators extending metrics: a short proof.Bull. Polish. Acad. Sci. 44 (1996), 267-269. Zbl 0866.54017, MR 1419399 |
| . |
