Abstract
Lindelöf numbers of sets Z⊂β(λ)∖λ are examined in Gδ-topologies (and in Gμ-topologies). The results are in a close connection to measurable and μ-strongly compact cardinal numbers. Those numbers are characterized by means of extensions of weakly complete filters, by τ-compactness of sets of certain complete ultrafilters and by Lindelöf numbers of the set of uniform ultrafilters in Gμ-topologies. Some known results about μ-strongly compact cardinals are reproved using set-theoretical methods.
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