Representing set-inclusion by embeddability (among the subspaces of the real line)

A. E. McCluskey; T.B.M. McMaster; W.S. Watson

doi:10.13025/24080

Representing set-inclusion by embeddability (among the subspaces of the real line)

A. E. McCluskey
, T.B.M. McMaster
, W.S. Watson

Mathematics

Queen's University of Belfast
York University

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

6 Citations (Scopus)

Abstract

We establish that the powerset ℘(ℝ) of the real line ℝ, ordered by set-inclusion, has the same ordertype as a certain subset of ℘(ℝ) ordered by homeomorphic embeddability. This is a contribution to the ongoing study of the possible ordertypes of subfamilies of ℘(ℝ) under embeddability, pioneered by Banach, Kuratowski and Sierpiński.

Original language	English
Pages (from-to)	89-92
Number of pages	4
Journal	General Topology and its Applications
Volume	96
Issue number	1
DOIs	https://doi.org/10.13025/24080 https://doi.org/10.1016/s0166-8641(98)00038-8
Publication status	Published - 1999

Keywords

G-sets
Ordering by homeomorphic embeddability
Partial order
Transfinite induction

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10.13025/24080Licence: CC BY-NC-ND
10.1016/s0166-8641(98)00038-8

Cite this

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AB - We establish that the powerset ℘(ℝ) of the real line ℝ, ordered by set-inclusion, has the same ordertype as a certain subset of ℘(ℝ) ordered by homeomorphic embeddability. This is a contribution to the ongoing study of the possible ordertypes of subfamilies of ℘(ℝ) under embeddability, pioneered by Banach, Kuratowski and Sierpiński.

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KW - Ordering by homeomorphic embeddability

KW - Partial order

KW - Transfinite induction

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JO - General Topology and its Applications

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IS - 1

ER -

Representing set-inclusion by embeddability (among the subspaces of the real line)

Abstract

Keywords

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