Elementary chains and compact spaces with a small diagonal

Journal article (2012)

Authors

Alan Dow University of North Carolina

K.P. Hart Analysis -

Research Group

Analysis () (TU Delft)

Small diagonal Metrizable Chains of elementary substructures

To reference this document use:

http://resolver.tudelft.nl/uuid:21332009-be02-4adc-8823-6ce701981504

More Info

expand_more

Published Date

2012

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

It is a well known open problem if, in View the MathML sourceZFC, each compact space with a small diagonal is metrizable. We explore properties of compact spaces with a small diagonal using elementary chains of substructures. We prove that ccc subspaces of such spaces have countable ππ-weight. We generalize a result of Gruenhage about spaces which are metrizably fibered. Finally we discover that if there is a Luzin set of reals, then every compact space with a small diagonal will have many points of countable character.

Files

9219800_u_elemChains_published... (pdf)

(pdf | 0.288 Mb)

Download not available