منابع مشابه
Extreme point axioms for closure spaces
A pair (X, ) of a finite set X and a closure operator : 2X → 2X is called a closure space. The class of closure spaces includes matroids as well as antimatroids. Associated with a closure space (X, ), the extreme point operator ex: 2X → 2X is defined as ex(A) = {p|p ∈ A,p / ∈ (A − {p})}. We give characterizations of extreme point operators of closure spaces, matroids and antimatroids, respectiv...
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The hierarchy of separation axioms that is familiar from topological spaces generalizes to spaces with an isotone and expansive closure function. Neither additivity nor idempotence of the closure function must be assumed.
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for an arbitrary original polygon P . Further, no other relations Pn_p = 0 (p7*pi or p2 • or £jfc) are satisfied by P ' if P remains general ( P ' has no higher than the &th degree of regularity). This is also seen from (16'), where 0(co) ^ 0 , Rn-P^0 (since P is general) ; therefore P ' n _ ^ 0 . In fact, no relations of any kind besides (18) are satisfied by P' = MP if P remains general. This...
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In the framework of ZF, i.e., Zermelo-Fraenkel set theory without the axiom of choice AC, we show that if the family of all non-empty, closed subsets of a metric space (X, d) has a choice function, then so does the family of all non-empty, open subsets of X. In addition, we establish that the converse is not provable in ZF. We also show that the statement “every subspace of the real line R with...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.04.034