On p-compact group topologies on direct sums of \mathbb Q

2019/04/11 by Matheus Koveroff Bellini, Vinicius de Oliveira Rodrigues, Bellini, Matheus Koveroff +3
Mathematics · #22A05 #54G20 #54H11 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Primary 54D20 #Secondary 54A35 #math.GN #math.GR #msc:22A05 #msc:54A35 #msc:54D20 #msc:54G20 #msc:54H11

paper · pdf · doi:10.48550/arxiv.1904.05928

arxiv created 2019/04/11 · arxiv updated 2019/04/15

Abstract

We prove that if p is a selective ultrafilter then \mathbb Q^(κ) has a p-compact group topology without non-trivial convergent sequences, for each infinite cardinal κ=κ^ω. In particular, this gives the first arbitrarily large examples of countably compact groups without non-trivial convergent sequences that are torsion-free.

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