On properties of compacta that do not reflect in small continuous images

Menachem Magidor; Grzegorz Plebanek

doi:10.1016/j.topol.2017.02.013

On properties of compacta that do not reflect in small continuous images

Menachem Magidor, Grzegorz Plebanek^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

3 Scopus citations

Abstract

Assuming that there is a stationary set of ordinals of countable cofinality in ω₂ that does not reflect, we prove that there exists a compact space which is not Corson compact and whose all continuous images of weight ≤ω₁ are Eberlein compacta. This yields an example of a Banach space of density ω₂ which is not weakly compactly generated but all its subspaces of density ≤ω₁ are weakly compactly generated. We also prove that under Martin's axiom countable functional tightness does not reflect in small continuous images of compacta.

Original language	English
Pages (from-to)	131-139
Number of pages	9
Journal	Topology and its Applications
Volume	220
DOIs	https://doi.org/10.1016/j.topol.2017.02.013
State	Published - 1 Apr 2017

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Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

Corson compact
Eberlein compact
Functional tightness
Reflection principle
Stationary set

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10.1016/j.topol.2017.02.013

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abstract = "Assuming that there is a stationary set of ordinals of countable cofinality in ω2 that does not reflect, we prove that there exists a compact space which is not Corson compact and whose all continuous images of weight ≤ω1 are Eberlein compacta. This yields an example of a Banach space of density ω2 which is not weakly compactly generated but all its subspaces of density ≤ω1 are weakly compactly generated. We also prove that under Martin's axiom countable functional tightness does not reflect in small continuous images of compacta.",

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N2 - Assuming that there is a stationary set of ordinals of countable cofinality in ω2 that does not reflect, we prove that there exists a compact space which is not Corson compact and whose all continuous images of weight ≤ω1 are Eberlein compacta. This yields an example of a Banach space of density ω2 which is not weakly compactly generated but all its subspaces of density ≤ω1 are weakly compactly generated. We also prove that under Martin's axiom countable functional tightness does not reflect in small continuous images of compacta.

AB - Assuming that there is a stationary set of ordinals of countable cofinality in ω2 that does not reflect, we prove that there exists a compact space which is not Corson compact and whose all continuous images of weight ≤ω1 are Eberlein compacta. This yields an example of a Banach space of density ω2 which is not weakly compactly generated but all its subspaces of density ≤ω1 are weakly compactly generated. We also prove that under Martin's axiom countable functional tightness does not reflect in small continuous images of compacta.

KW - Corson compact

KW - Eberlein compact

KW - Functional tightness

KW - Reflection principle

KW - Stationary set

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VL - 220

SP - 131

EP - 139

JO - Topology and its Applications

JF - Topology and its Applications

ER -

On properties of compacta that do not reflect in small continuous images

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