A NOTE ON PARACOMPACT p-SPACES AND THE MONOTONE D-PROPERTY

Publisher： Cambridge University Press

E-ISSN： 1755-1633|83|3|463-469

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.83, Iss.3, 2011-02, pp. : 463-469

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Abstract

For any generalized ordered space X with the underlying linearly ordered topological space Xu, let X* be the minimal closed linearly ordered extension of X and $\tilde {X}$ be the minimal dense linearly ordered extension of X. The following results are obtained. The projection mapping π:X*→X, π(〈x,i〉)=x, is closed.The projection mapping $\phi : \tilde {X} \rightarrow X_u$, ϕ(〈x,i〉)=x, is closed.X* is a monotone D-space if and only if X is a monotone D-space.$\tilde {X}$ is a monotone D-space if and only if Xu is a monotone D-space.For the Michael line M, $\tilde {M}$ is a paracompact p-space, but not continuously Urysohn.

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