A solution to a problem about the Erdos space

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ÖNAL S., Soyarslan S.

Fundamenta Mathematicae, cilt.259, sa.2, ss.207-211, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 259 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.4064/fm192-4-2022
  • Dergi Adı: Fundamenta Mathematicae
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.207-211
  • Anahtar Kelimeler: Erd?s space, topological group, sequence space
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

© 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.