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  • Closure operator  (1)
  • arrow relation  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Finding all closed sets: A general approach (1991)
    Springer
    Order 8 (1991), S. 283-290 
    Details
    ISSN: 1572-9273
    Keywords: 06A15 ; 68RXX ; Closure operator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present a unifying theoretical and algorithmic approach to the problems to determine all closed sets of a closure operator, to do this up to isomorphism, and to determine the elements of certain ideals of a power set. This will be done by generalizing the concept of closure operators using the interplay of several orders of a power set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00383449
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Removing critical pairs (1989)
    Springer
    Order 6 (1989), S. 107-118 
    Details
    ISSN: 1572-9273
    Keywords: Order dimension ; critical pair ; Ferrers dimension ; arrow relation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A long-standing conjecture in dimension theory asserts that every ordered set with at least three elements contains two elements whose removal decreases the dimension by at most one. We disprove the yet stronger conjecture that the removal of any critical pair decreases the dimension by at most one. We have constructed the counterexample using Ferrers dimension which will be described in this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02034329
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    Paper (German National Licenses)
    Fulltext
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