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A NOTE ON PARACOMPACT p-SPACES AND THE MONOTONE D-PROPERTY
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 83 / Issue 3 / June 2011
- Published online by Cambridge University Press:
- 07 February 2011, pp. 463-469
- Print publication:
- June 2011
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- Article
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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
be the minimal dense linearly ordered extension of X. The following results are obtained. (1) The projection mapping π:X*→X, π(〈x,i〉)=x, is closed.
(2) The projection mapping
, ϕ(〈x,i〉)=x, is closed.(3) X* is a monotone D-space if and only if X is a monotone D-space.
(4)
is a monotone D-space if and only if Xu is a monotone D-space.(5) For the Michael line M,
is a paracompact p-space, but not continuously Urysohn.
be the minimal dense linearly ordered extension of 
, ϕ(〈
is a paracompact 