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A note on the weak topology of spaces \(C_k(X)\) of continuous functions

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

It is well known that the property of being a bounded set in the class of topological vector spaces E is not a topological property, where a subset \(B\subset E\) is called a bounded set if every neighbourhood of zero U in E absorbs B. The paper deals with the problem which topological properties of bounded sets for the space \(C_{k}(X)\) (of continuous real-valued functions on a Tychonoff space X with the compact-open topology) endowed with the weak topology of \(C_{k}(X)\) can be transferred to bounded sets of \(C_{k}(Y)\) endowed with the weak topology, assuming that the corresponding weak topologies of both \(C_{k}(X)\) and \(C_{k}(Y)\) are homeomorphic.

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Acknowledgements

The authors wish to thank to prof. J. C. Ferrando for carefully reading the article and his remarks

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Adam Mickiewicz University, 61-614, Poznań, Poland

    Jerzy Ka̧kol

  2. Institute of Mathematics of the Czech Academy of Sciences, Prague, Czech Republic

    Jerzy Ka̧kol

  3. Universitat Politècnica de València, Camino de Vera s.n, 46022, Valencia, Spain

    Santiago Moll-López

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  1. Jerzy Ka̧kol
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  2. Santiago Moll-López
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Correspondence to Santiago Moll-López.

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The first named author is supported by the GAČR project 20-22230L RVO: 67985840.

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Ka̧kol, J., Moll-López, S. A note on the weak topology of spaces \(C_k(X)\) of continuous functions. RACSAM 115, 125 (2021). https://doi.org/10.1007/s13398-021-01051-1

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  • DOI: https://doi.org/10.1007/s13398-021-01051-1

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