Order

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

Splittability for Partially Ordered Sets

  • A. J. Hanna
  • T. B. M. McMaster
Article
  • 31 Downloads

Abstract

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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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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