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

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    0542801 - MÚ 2022 RIV ES eng J - Journal Article
    Kąkol, Jerzy - Moll-López, S.
    A note on the weak topology of spaces C_k(X) of continuous functions.
    Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Roč. 115, č. 3 (2021), č. článku 125. ISSN 1578-7303. E-ISSN 1579-1505
    R&D Projects: GA ČR(CZ) GF20-22230L
    Institutional support: RVO:67985840
    Keywords : weak topology * convex space
    OECD category: Pure mathematics
    Impact factor: 2.276, year: 2021
    Method of publishing: Limited access
    https://doi.org/10.1007/s13398-021-01051-1

    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⊂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 Ck(X) (of continuous real-valued functions on a Tychonoff space X with the compact-open topology) endowed with the weak topology of Ck(X) can be transferred to bounded sets of Ck(Y) endowed with the weak topology, assuming that the corresponding weak topologies of both Ck(X) and Ck(Y) are homeomorphic.
    Permanent Link: http://hdl.handle.net/11104/0320146

     
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