Three-point sets

K. Bouhjar; J.J. Dijkstra; J. van Mill

doi:10.1016/S0166-8641(99)00232-1

Three-point sets

K. Bouhjar
, J.J. Dijkstra
, J. van Mill

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

We prove that a planar set which meets each line in exactly three points cannot contain a continuum and cannot be an F-sigma-set. We also present some results on extending and splitting n-point sets. Our results imply that there is a four-point set which contains an are. (C) 2001 Elsevier Science B.V. All rights reserved.

Original language	English
Pages (from-to)	215-227
Journal	Topology and its Applications
Volume	112
Issue number	2
DOIs	https://doi.org/10.1016/S0166-8641(99)00232-1
Publication status	Published - 2001

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 16 Peace, Justice and Strong Institutions

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10.1016/S0166-8641(99)00232-1

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title = "Three-point sets",

abstract = "We prove that a planar set which meets each line in exactly three points cannot contain a continuum and cannot be an F-sigma-set. We also present some results on extending and splitting n-point sets. Our results imply that there is a four-point set which contains an are. (C) 2001 Elsevier Science B.V. All rights reserved.",

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AU - Bouhjar, K.

AU - Dijkstra, J.J.

AU - van Mill, J.

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AB - We prove that a planar set which meets each line in exactly three points cannot contain a continuum and cannot be an F-sigma-set. We also present some results on extending and splitting n-point sets. Our results imply that there is a four-point set which contains an are. (C) 2001 Elsevier Science B.V. All rights reserved.

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UR - https://www.scopus.com/pages/publications/0037985286#tab=citedBy

U2 - 10.1016/S0166-8641(99)00232-1

DO - 10.1016/S0166-8641(99)00232-1

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VL - 112

SP - 215

EP - 227

JO - Topology and its Applications

JF - Topology and its Applications

IS - 2

ER -

Three-point sets

Abstract

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