The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
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Alexander V. Osipov
Abstract
A topological space X is Baire if the intersection of any sequence of open dense subsets of X is dense in X. In this paper, we establish that the property (κ) for a Tychonoff space X is equivalent to Baireness of B1(X), and hence, the Banakh property for Cp(X) is equivalent to meagerness of B1(X). Thus, we obtain one characteristic of the Banakh property for Cp(X) through the property of the space X.
Funding statement: The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2025-1549).
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(Communicated by L’ubica Holá)
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- Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
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