The zoom link is: https://pitt.zoom.us/j/96207413067
(meeting id 962 0741 3067)
Abstract or Additional Information
For a space X, let K(X) denote the family of all compact subsets of X. Ziqin Feng and Paul Gartside introduced a Tukey-type order defined via compact covers of spaces: in this setting, a space X is said to be Tukey above a space Y if there exists a map from K(X) to K(Y) which sends compact covers of X to compact covers of Y.
They showed that, in the class of separable metrizable spaces, a space is Menger if and only if it is not Tukey above the Baire space ω^ω.
They asked (Question 3.5) whether this equivalence remains true in the class of general Lindelöf spaces.
The aim of the talk is to show that the equivalence holds in a wider class of spaces, and also to present a counterexample demonstrating that it does not hold in full generality.
This is a joint work with M. Bonanzinga, D. Giacopello, and B. Tsaban.
Reference: Z. Feng, P. Gartside, The Shape of Compact Covers, Journal of Symbolic Logic, 2024, 1–15, https://doi.org/10.1017/jsl.2024.53