Complete lattices and the generalized Cantor theorem
نویسندگان
چکیده
منابع مشابه
Cantor-bernstein Theorem for Lattices
This paper is a continuation of a previous author’s article; the result is now extended to the case when the lattice under consideration need not have the least element.
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A well known theorem of Cantor asserts that the cardinal of the power-set of a given set always exceeds the cardinal of the original set. An analogous result for sets having additional structure is the well known theorem that the set of initial segments of a well ordered set always has order type greater than the original set. These two theorems suggest that there should be a similar result for...
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We consider complete lattices equipped with preorderings indexed by the ordinals less than a given (limit) ordinal subject to certain axioms. These structures, called stratified complete lattices, and weakly monotone functions over them, provide a framework for solving fixed point equations involving non-monotone operations such as negation or complement, and have been used to give semantics to...
متن کاملBasic Theorem for Generalized One-sided Concept Lattices
The Basic Theorem for Concept Lattices represents one of the fundamental tool for a theoretical study of concept lattices. In this paper the similar assertion for generalized one-sided concept lattices is derived. Mathematics Subject Classification: 06A15
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Given two finite sets, questions about the existence of different types of functions between these two sets are easy to solve, as there are finitely many such functions and so one many simply enumerate them. Further more, if one has two injective functions then it is intuitively obvious that both such functions are bijections (although not necessarily the inverses of each other). However, when ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0268091-0