On the lexicographic dimension of linearly ordered sets
V. Novák (1964)
Fundamenta Mathematicae
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V. Novák (1964)
Fundamenta Mathematicae
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K. Padmavally (1955)
Fundamenta Mathematicae
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Ai-Jun Xu (2015)
Open Mathematics
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In this paper, we show that any generalized ordered space X is monotonically (countably) metacompact if and only if the subspace X - { x } is monotonically (countably) metacompact for every point x of X and monotone (countable) metacompact property is hereditary with respect to convex (open) subsets in generalized ordered spaces. In addition, we show the equivalence of two questions posed by H.R. Bennett, K.P. Hart and D.J. Lutzer.
Edwin Miller (1936)
Fundamenta Mathematicae
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Arens, Richard (1951)
Portugaliae mathematica
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Vítězslav Novák, Miroslav Novotný (2000)
Czechoslovak Mathematical Journal
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A construction is given which makes it possible to find all linear extensions of a given ordered set and, conversely, to find all orderings on a given set with a prescribed linear extension. Further, dense subsets of ordered sets are studied and a procedure is presented which extends a linear extension constructed on a dense subset to the whole set.
Kent, Darrell C., Richmond, T.A. (1990)
International Journal of Mathematics and Mathematical Sciences
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Milan R. Tasković (1980)
Publications de l'Institut Mathématique
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