Geodesic
Non-metric Rim-metrizable Continua and Unique Hyperspace
Publications de l'Institut Mathématique, _N_S_73 (2003) no. 87, p. 97

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

A class $\Lambda$ of continua is said to be $C$\textit{-determined} provided that if $X,Y\in\Lambda$ and $C(X)\approx C(Y)$, then $X\approx Y$. A continuum $X$ has \textit{unique hyperspace} provided that if $Y$ is a continuum and $C(X)\approx C(Y)$, then $X\approx Y$. In the realm of metric continua the following classes of continua are known to have unique hyperspace: hereditarily indecomposable continua, smooth fans (in the class of fans) and indecomposable continua whose proper and non-degenerate subcontinua are arcs. We prove that these classes have unique hyperspace in the realm of rim-metrizable non-metric continua.
DOI : 10.2298/PIM0373097L
Classification : 54B20 54B35
Keywords: hyperspace, continuum, inverse system 
@article{10_2298_PIM0373097L,
     author = {Ivan Lon\v{c}ar},
     title = {Non-metric {Rim-metrizable} {Continua} and {Unique} {Hyperspace}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {97 },
     publisher = {mathdoc},
     volume = {_N_S_73},
     number = {87},
     year = {2003},
     doi = {10.2298/PIM0373097L},
     zbl = {1054.54026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0373097L/}
}
TY  - JOUR
AU  - Ivan Lončar
TI  - Non-metric Rim-metrizable Continua and Unique Hyperspace
JO  - Publications de l'Institut Mathématique
PY  - 2003
SP  - 97 
VL  - _N_S_73
IS  - 87
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM0373097L/
DO  - 10.2298/PIM0373097L
LA  - en
ID  - 10_2298_PIM0373097L
ER  - 
%0 Journal Article
%A Ivan Lončar
%T Non-metric Rim-metrizable Continua and Unique Hyperspace
%J Publications de l'Institut Mathématique
%D 2003
%P 97 
%V _N_S_73
%N 87
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM0373097L/
%R 10.2298/PIM0373097L
%G en
%F 10_2298_PIM0373097L
Ivan Lončar. Non-metric Rim-metrizable Continua and Unique Hyperspace. Publications de l'Institut Mathématique, _N_S_73 (2003) no. 87, p. 97 . doi: 10.2298/PIM0373097L

Cité par Sources :