A solution to a problem about the Erdos space

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ÖNAL S., Soyarslan S.

Fundamenta Mathematicae, vol.259, no.2, pp.207-211, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 259 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.4064/fm192-4-2022
  • Journal Name: Fundamenta Mathematicae
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.207-211
  • Keywords: Erd?s space, topological group, sequence space
  • Middle East Technical University Affiliated: Yes

Abstract

© Instytut Matematyczny PAN, 2022.For the Erdos space, (E; τ ), let us define a new topology, τclopen, generated by all clopen subsets of E. A. V. Arhangel'skii and J. van Mill asked whether the topology τclopen is compatible with the group structure on E. In this paper, we give a negative answer to this question by showing that there exists a clopen subset O of E such that 0 2 O and K + U ⊆ O for every unbounded set K of E and every set U ∈ τ containing 0.