, Volume 17, Issue 4, pp 343–351 | Cite as

Splittability for Partially Ordered Sets

  • A. J. Hanna
  • T. B. M. McMaster


A topological space X is said to be splittable over a class P of spaces if for every AX there exists continuous f:XYP such that f(A)∩f(XA) is empty. A class P of topological spaces is said to be a splittability class if the spaces splittable over P are precisely the members of P. We extend the notion of splittability to partially ordered sets and consider splittability over some elementary posets. We identify precisely which subsets of a poset can be split along over an n-point chain. Using these results it is shown that the union of two splittability classes need not be a splittability class and a necessary condition for P to be a splittability class is given.

partially ordered set splittability 


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  1. 1.
    Arhangel'ski?, A. V. (1985) A general concept of cleavability of topological spaces over a class of spaces, in Abstracts Tiraspol Symposium (Stiinca, Kishinev), pp. 8-10 (in Russian).Google Scholar
  2. 2.
    Arhangel'ski?, A. V. (1993) A survey of cleavability, Topology Appl. 54, 141-163.Google Scholar
  3. 3.
    Marron, D. J. (1997) Splittability in ordered sets and in ordered spaces, Ph.D. Thesis, Queen's University of Belfast.Google Scholar
  4. 4.
    Marron, D. J. andMcMaster, T. B. M., Cleavability in semigroups, Semigroup Forum, to appear.Google Scholar
  5. 5.
    Marron, D. J. and McMaster, T. B. M., Splittability for ordered topological spaces, Boll. Un. Mat. Ital., to appear.Google Scholar
  6. 6.
    McCartan, S. D. (1979) Minimal T ES-spaces and minimal T EF-spaces, Proc. Roy. Irish Acad. Sect. A 79(2), 11-13.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • A. J. Hanna
    • 1
  • T. B. M. McMaster
    • 2
  1. 1.Department of Pure MathematicsThe Queen's University of Belfast, BelfastBelfastU.K.
  2. 2.Department of Pure MathematicsThe Queen's University of Belfast, BelfastBelfastU.K.

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