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2 results

  • CONTINUITY ON GENERALISED TOPOLOGICAL SPACES VIA HEREDITARY CLASSES

  • Part of
  • P. MONTAGANTIRUD, W. THAIKUA
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 97 / Issue 2 / April 2018
    Published online by Cambridge University Press:
    21 February 2018, pp. 320-330
    Print publication:
    April 2018
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  • A generalised topology is a collection of subsets of a given nonempty set containing the empty set and arbitrary unions of the elements in the collection. By using the concept of hereditary classes, a generalised topology can be extended to a new one, called a generalised topology via a hereditary class. We study continuity on generalised topological spaces via hereditary classes in various situations.

  • Continuous Images of Compact Semilattices

  • Murray Bell, Jan Pelant
  • Journal:
    Canadian Mathematical Bulletin / Volume 30 / Issue 1 / 01 March 1987
    Published online by Cambridge University Press:
    20 November 2018, pp. 109-113
    Print publication:
    01 March 1987
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  • Hyadic spaces are the continuous images of a hyperspace of a compact space. We prove that every non-isolated point in a hyadic space is the endpoint of some infinite cardinal subspace. We isolate a more general order-theoretic property of hyerspaces of compact spaces which is also enjoyed by compact semilattices from which the theorem follows.