A subspace of ℝ3 for which Cmp ≠ def

Michael Levin; Jack Segal

doi:10.1016/s0166-8641(97)00279-4

A subspace of ℝ³ for which Cmp ≠ def

Michael Levin, Jack Segal

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

3 Scopus citations

Abstract

We construct a separable metric space E in ℝ³ for which both the small and large compactness degrees cmp E = Cmp E = 1 and the compactness deficiency def E = 2. This improves on the example in ℝ⁴ given by R. Pol (1992) as a counterexample to the well-known conjecture of J. de Groot.

Original language	English
Pages (from-to)	165-168
Number of pages	4
Journal	Topology and its Applications
Volume	95
Issue number	2
DOIs	https://doi.org/10.1016/s0166-8641(97)00279-4
State	Published - 1 Jan 1999
Externally published	Yes

Keywords

Compactness deficiency
Compactness degree
De Groot's conjecture

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1016/s0166-8641(97)00279-4

Cite this

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abstract = "We construct a separable metric space E in ℝ3 for which both the small and large compactness degrees cmp E = Cmp E = 1 and the compactness deficiency def E = 2. This improves on the example in ℝ4 given by R. Pol (1992) as a counterexample to the well-known conjecture of J. de Groot.",

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AU - Segal, Jack

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N2 - We construct a separable metric space E in ℝ3 for which both the small and large compactness degrees cmp E = Cmp E = 1 and the compactness deficiency def E = 2. This improves on the example in ℝ4 given by R. Pol (1992) as a counterexample to the well-known conjecture of J. de Groot.

AB - We construct a separable metric space E in ℝ3 for which both the small and large compactness degrees cmp E = Cmp E = 1 and the compactness deficiency def E = 2. This improves on the example in ℝ4 given by R. Pol (1992) as a counterexample to the well-known conjecture of J. de Groot.

KW - Compactness deficiency

KW - Compactness degree

KW - De Groot's conjecture

UR - https://www.scopus.com/pages/publications/0010206361

U2 - 10.1016/s0166-8641(97)00279-4

DO - 10.1016/s0166-8641(97)00279-4

M3 - Article

AN - SCOPUS:0010206361

SN - 0016-660X

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EP - 168

JO - Topology and its Applications

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