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Diagonal conditions in ordered spaces

Harold Bennett, David Lutzer (1997)

Fundamenta Mathematicae

For a space X and a regular uncountable cardinal κ ≤ |X| we say that κ ∈ D(X) if for each T X 2 - Δ ( X ) with |T| = κ, there is an open neighborhood W of Δ(X) such that |T - W| = κ. If ω 1 D ( X ) then we say that X has a small diagonal, and if every regular uncountable κ ≤ |X| belongs to D(X) then we say that X has an H-diagonal. In this paper we investigate the interplay between D(X) and topological properties of X in the category of generalized ordered spaces. We obtain cardinal invariant theorems and metrization theorems...

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