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The space \(C_p(X)\) is cofinally Polish if and only if it is pseudocomplete

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

Abstract

We prove that \(C_p(X)\) is pseudocomplete if and only if it has a dense cofinally Polish subspace. This result provides positive answers to two open questions from (Niknejad in Bull Belg Math Soc 25(3):439–452, 2018). We also establish that a space X is cofinally Polish if and only if its Hewitt extension \(\upsilon X\) is cofinally Polish and show that a subspace X of an ordinal is cofinally Polish if and only if X has countable extent.

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  1. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco, 186 Col. Vicentina, Iztapalapa, C.P. 09340, Mexico D.F., Mexico

    V. V. Tkachuk

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  1. V. V. Tkachuk
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Correspondence to V. V. Tkachuk.

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Tkachuk, V.V. The space \(C_p(X)\) is cofinally Polish if and only if it is pseudocomplete. RACSAM 115, 68 (2021). https://doi.org/10.1007/s13398-021-01005-7

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  • DOI: https://doi.org/10.1007/s13398-021-01005-7

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