Perfect GO-spaces which have a perfect linearly ordered extension

2009

Bull. Aust. Math. Soc.

Self Cite

We show that for the Sorgenfrey line S, the minimal dense linearly ordered extension of S is a D-space, but not a monotone D-space; the minimal closed linearly ordered extension of S is not a monotone D-space; the monotone D-property is inversely preserved by finite-to-one closed mappings, but cannot be inversely preserved by perfect mappings.2000 Mathematics subject classification: primary 54D20; secondary 54F05, 54G15, 54C25.

“…The space S * is called a closed linearly ordered extension of S (see [3]). By [6,Theorem 9], the space S * is the minimal closed linearly ordered extension of S.…”

Section: Resultsmentioning

confidence: 99%

THE D-PROPERTY AND THE SORGENFREY LINE

Gao

2009

Bull. Aust. Math. Soc.

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“…By the proof of Theorem 4, it is known that if the GO-space X has a σ-discrete dense subset, then X satisfies the conditions of Theorem 1. With R, L and I as in Section 1, by the proof of Theorem 1 (see [5]), there exists a σ-discrete set F of X such that I ⊂ F ⊂ R ∪ L ∪ I, and the perfect linearly ordered extension of X constructed in [5] has the form…”

Section: Theoremmentioning

confidence: 99%

Extensions of perfect GO-spaces and $\sigma $-discrete dense sets

1999

Proc. Amer. Math. Soc.

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“…By [5,Proposition 2.7],X is the minimal dense linearly ordered extension of X and, by [7,Theorem 9], X * is the minimal closed linearly ordered extension of X .…”

mentioning

confidence: 99%

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

Gao

2011

Bull. Aust. Math. Soc.

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For any generalized ordered space X with the underlying linearly ordered topological space X u , let X * be the minimal closed linearly ordered extension of X andX be the minimal dense linearly ordered extension of X . The following results are obtained.(1)The projection mapping π :The projection mapping φ :X → X u , φ( x, i ) = x, is closed. 2010 Mathematics subject classification: primary 54C10; secondary 54C25, 54D20, 54D30, 54F05.