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Gδ Sets IN σ-IDEALS GENERATED BY COMPACT SETS

Published online by Cambridge University Press:  04 March 2019

MAYA SARAN
MAYA SARAN*
Affiliation:
DEPARTMENT OF MATHEMATICS ASHOKA UNIVERSITY RAJIV GANDHI EDUCATION CITY SONEPAT, HARYANA131029, INDIA E-mail: [email protected]
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Abstract

Given a compact Polish space E and the hyperspace of its compact subsets ${\cal K}\left( E \right)$, we consider Gδσ-ideals of compact subsets of E. Solecki has shown that any σ-ideal in a broad natural class of Gδ ideals can be represented via a compact subset of ${\cal K}\left( E \right)$; in this article we examine the behaviour of Gδ subsets of E with respect to the representing set. Given an ideal I in this class, we construct a representing set that recognises a compact subset of E as being “small” precisely when it is in I, and recognises a Gδ subset of E as being “small” precisely when it is covered by countably many compact sets from I.

Keywords

03E1528A0554H05descriptive set theoryideals of compact sets
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 2 , June 2019 , pp. 781 - 797
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

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