A solution to a problem about the Erdos space

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2022-1-01

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Önal, Süleyman
Soyarslan, Servet

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© 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.

Subject Keywords

Erd?s space, topological group, sequence space, Erdos space, sequence space, topological group

URI

https://hdl.handle.net/11511/101826

Journal

Fundamenta Mathematicae

DOI

https://doi.org/10.4064/fm192-4-2022

Collections

Department of Mathematics, Article

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Citation Formats

S. Önal and S. Soyarslan, “A solution to a problem about the Erdos space,” Fundamenta Mathematicae, vol. 259, no. 2, pp. 207–211, 2022, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/101826.