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 University Press

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
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