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1 results

  • Separators in Continuous Images of Ordered Continua and Hereditarily Locally Connected Continua

  • J. Grispolakis, J. Nikiel, J. N. Simone, E. D. Tymchatyn
  • Journal:
    Canadian Mathematical Bulletin / Volume 36 / Issue 2 / 01 June 1993
    Published online by Cambridge University Press:
    20 November 2018, pp. 154-163
    Print publication:
    01 June 1993
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  • 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.