Geodesic
Separators in Continuous Images of Ordered Continua and Hereditarily Locally Connected Continua
Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 154-163

Voir la notice de l'article provenant de la source Cambridge

DOI

Let X be a Hausdorff space which is the continuous image of an ordered continuum. We prove that every irreducible separator of X is metrizable. This is a far reaching extension of the 1967 theorem of S. Mardešić which asserts that X has a basis of open sets with metrizable boundaries. Our first result is then used to show that, in particular, if Y is an hereditarily locally connected continuum, then for subsets of Y quasi-components coincide with components, and that the boundary of each connected open subset of Y is accessible by ordered continua. These results answer open problems in the literature due to the fourth and third authors, respectively.
DOI : 10.4153/CMB-1993-023-1
Mots-clés : 54F15, 54C05, 54F05, 54F50, ordered continuum, continuous image, hereditarily locally connectedcontinuum, component, quasi-component, accessible, irreducible separator, totally disconnected 
Grispolakis, J.; Nikiel, J.; Simone, J. N.; Tymchatyn, E. D. Separators in Continuous Images of Ordered Continua and Hereditarily Locally Connected Continua. Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 154-163. doi: 10.4153/CMB-1993-023-1
@article{10_4153_CMB_1993_023_1,
     author = {Grispolakis, J. and Nikiel, J. and Simone, J. N. and Tymchatyn, E. D.},
     title = {Separators in {Continuous} {Images} of {Ordered} {Continua} and {Hereditarily} {Locally} {Connected} {Continua}},
     journal = {Canadian mathematical bulletin},
     pages = {154--163},
     year = {1993},
     volume = {36},
     number = {2},
     doi = {10.4153/CMB-1993-023-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-023-1/}
}
TY  - JOUR
AU  - Grispolakis, J.
AU  - Nikiel, J.
AU  - Simone, J. N.
AU  - Tymchatyn, E. D.
TI  - Separators in Continuous Images of Ordered Continua and Hereditarily Locally Connected Continua
JO  - Canadian mathematical bulletin
PY  - 1993
SP  - 154
EP  - 163
VL  - 36
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-023-1/
DO  - 10.4153/CMB-1993-023-1
ID  - 10_4153_CMB_1993_023_1
ER  - 
%0 Journal Article
%A Grispolakis, J.
%A Nikiel, J.
%A Simone, J. N.
%A Tymchatyn, E. D.
%T Separators in Continuous Images of Ordered Continua and Hereditarily Locally Connected Continua
%J Canadian mathematical bulletin
%D 1993
%P 154-163
%V 36
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-023-1/
%R 10.4153/CMB-1993-023-1
%F 10_4153_CMB_1993_023_1

Cité par Sources :