Not every transitively D-space is D

Duncan Dauvergne

doi:10.1016/j.topol.2016.06.002

Not every transitively D-space is D

Duncan Dauvergne

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In 2008, Liang-Xue Peng defined a weakening of the D-space property known as the transitively D property. He asked whether or not every transitively D-space is D. We show that three different examples of linearly Lindelöf, non-Lindelöf spaces are transitively D but not D, answering Peng's question in the negative.

Original language	English (US)
Pages (from-to)	115-119
Number of pages	5
Journal	Topology and its Applications
Volume	209
DOIs	https://doi.org/10.1016/j.topol.2016.06.002
State	Published - Aug 15 2016

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

D-spaces
Linearly Lindelöf spaces
Transitively D-spaces

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10.1016/j.topol.2016.06.002

Cite this

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abstract = "In 2008, Liang-Xue Peng defined a weakening of the D-space property known as the transitively D property. He asked whether or not every transitively D-space is D. We show that three different examples of linearly Lindel{\"o}f, non-Lindel{\"o}f spaces are transitively D but not D, answering Peng's question in the negative.",

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AB - In 2008, Liang-Xue Peng defined a weakening of the D-space property known as the transitively D property. He asked whether or not every transitively D-space is D. We show that three different examples of linearly Lindelöf, non-Lindelöf spaces are transitively D but not D, answering Peng's question in the negative.

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KW - Transitively D-spaces

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SP - 115

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ER -

Not every transitively D-space is D

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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