Displaying similar documents to “Calibres, compacta and diagonals”

Notes on monotonically metacompact generalized ordered spaces

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.

The Gruenhage property, property *, fragmentability, and σ-isolated networks in generalized ordered spaces

Harold Bennett, David Lutzer (2013)

Fundamenta Mathematicae

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We examine the Gruenhage property, property * (introduced by Orihuela, Smith, and Troyanski), fragmentability, and the existence of σ-isolated networks in the context of linearly ordered topological spaces (LOTS), generalized ordered spaces (GO-spaces), and monotonically normal spaces. We show that any monotonically normal space with property * or with a σ-isolated network must be hereditarily paracompact, so that property * and the Gruenhage property are equivalent in monotonically...

Relatively complemented ordered sets

Ivan Chajda, Zuzana Morávková (2000)

Discussiones Mathematicae - General Algebra and Applications

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We investigate conditions for the existence of relative complements in ordered sets. For relatively complemented ordered sets with 0 we show that each element b ≠ 0 is the least one of the set of all upper bounds of all atoms contained in b.

On generalized ordered spaces

D. J. Lutzer

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1. Introduction................................................................................................................52. Characterization of generalized ordered spaces ..............................................73. Technical lemmas ..................................................................................................94. Paracompactness in GO spaces..........................................................................115. Metrizability and related properties...

Linear extensions of orderings

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.

Completion of a half linearly cyclically ordered group

Štefan Černák (2002)

Discussiones Mathematicae - General Algebra and Applications

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The notion of a half lc-group G is a generalization of the notion of a half linearly ordered group. A completion of G by means of Dedekind cuts in linearly ordered sets and applying Świerczkowski's representation theorem of lc-groups is constructed and studied.