An elementary counterexample on dense normality

Aisling E. McCluskey; T.B.M. McMaster

doi:10.13025/23427

An elementary counterexample on dense normality

Aisling E. McCluskey
, T.B.M. McMaster

Mathematics

Queen's University of Belfast

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

We show that the Sorgenfrei plane is not normal on any of its dense subsets, that is, is not densely normal. This addresses in the simplest possible terms Arhangel'skii's question as to whether an elementary example exists of a regular κ-normal space that fails to be densely normal.

Original language	English
Pages (from-to)	87-90
Number of pages	4
Journal	Topology and its Applications
Volume	130
Issue number	1
DOIs	https://doi.org/10.13025/23427 https://doi.org/10.1016/s0166-8641(02)00200-6
Publication status	Published - 15 Apr 2003

Keywords

Densely normal
Sorgenfrei plane
κ-normal

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10.13025/23427Licence: CC BY-NC-ND
10.1016/s0166-8641(02)00200-6

Cite this

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abstract = "We show that the Sorgenfrei plane is not normal on any of its dense subsets, that is, is not densely normal. This addresses in the simplest possible terms Arhangel'skii's question as to whether an elementary example exists of a regular κ-normal space that fails to be densely normal.",

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AB - We show that the Sorgenfrei plane is not normal on any of its dense subsets, that is, is not densely normal. This addresses in the simplest possible terms Arhangel'skii's question as to whether an elementary example exists of a regular κ-normal space that fails to be densely normal.

KW - Densely normal

KW - Sorgenfrei plane

KW - κ-normal

UR - http://hdl.handle.net/10379/9507

UR - https://www.scopus.com/pages/publications/0038350877

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JF - Topology and its Applications

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An elementary counterexample on dense normality

Abstract

Keywords

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