On linear functorial operators extending pseudometrics

Banakh, Taras O., and Pikhurko, Oleg. "On linear functorial operators extending pseudometrics." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 343-348. <http://eudml.org/doc/248082>.

@article{Banakh1997,
abstract = {For a functor $F\supset Id$ on the category of metrizable compacta, we introduce a conception of a linear functorial operator $T=\lbrace T_X:Pc(X)\rightarrow Pc(FX)\rbrace $ 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 $\lbrace 1,\dots ,n\rbrace $ 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.},
author = {Banakh, Taras O., Pikhurko, Oleg},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {linear functorial operator extending (pseudo)metrics; the functor of $G$-symmetric power; linear functorial operator extending pseudometrics; functor of -symmetric power},
language = {eng},
number = {2},
pages = {343-348},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On linear functorial operators extending pseudometrics},
url = {http://eudml.org/doc/248082},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Banakh, Taras O.
AU - Pikhurko, Oleg
TI - On linear functorial operators extending pseudometrics
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 2
SP - 343
EP - 348
AB - For a functor $F\supset Id$ on the category of metrizable compacta, we introduce a conception of a linear functorial operator $T=\lbrace T_X:Pc(X)\rightarrow Pc(FX)\rbrace $ 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 $\lbrace 1,\dots ,n\rbrace $ 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.
LA - eng
KW - linear functorial operator extending (pseudo)metrics; the functor of $G$-symmetric power; linear functorial operator extending pseudometrics; functor of -symmetric power
UR - http://eudml.org/doc/248082
ER -