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Quasicontinuous Subcontinuous Functions and Compactness

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Abstract

Let X be a locally compact space and (Y, d) be a metric space. A subfamily \({\mathcal E}\) of the space of quasicontinuous subcontinuous functions from X to Y is compact in this space equipped with the topology of uniform convergence on compact sets if and only if \({\mathcal E}\) is closed, compactly bounded and densely equiquasicontinuous. This result is a new version of Ascoli-type theorem for quasicontinuous subcontinuous functions.

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Authors and Affiliations

  1. Academy of Sciences, Institute of Mathematics, Štefánikova 49, 81473, Bratislava, Slovakia

    Ľubica Holá

  2. Department of Mathematics and Computer Science Faculty of Education, Trnava University, Priemyselná 4, 918 43, Trnava, Slovakia

    Dušan Holý

Authors
  1. Ľubica Holá
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  2. Dušan Holý
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Correspondence to Ľubica Holá.

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Holá, Ľ., Holý, D. Quasicontinuous Subcontinuous Functions and Compactness. Mediterr. J. Math. 13, 4509–4518 (2016). https://doi.org/10.1007/s00009-016-0759-8

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  • DOI: https://doi.org/10.1007/s00009-016-0759-8

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