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Some remarks on Sierpiński–Zygmund functions in the strong sense

  • Alexander Kharazishvili EMAIL logo

Abstract

For certain families of topologies, the existence of a common Sierpiński–Zygmund function (of a common Sierpiński–Zygmund function in the strong sense) is established. In this connection, the notion of a Sierpiński–Zygmund space (of a Sierpiński–Zygmund space in the strong sense) is introduced and examined. The behavior of such spaces under some standard topological operations is considered.

MSC 2010: 26A15; 26A21; 26A30

Award Identifier / Grant number: FR-18-6190

Funding statement: This work was partially supported by Shota Rustaveli National Science Foundation, Grant number FR-18-6190.

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Received: 2018-09-27
Accepted: 2019-01-17
Published Online: 2020-04-15
Published in Print: 2020-12-01

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