Abstract
We study the property of separability of functional space C(X) with the open-point and bi-point-open topologies and show that it is consistent with ZFC that there is a set of reals of cardinality \({\mathfrak{c}}\) such that a set C(X) with the open-point topology is not a separable space. We also show in a set model (the iterated perfect set model) that for every set of reals X, C(X) with the bi-point-open topology is a separable space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Jindal A., McCoy R. A., Kundu S.: The open-point and bi-point-open topologies on C(X): Submetrizability and cardinal functions. Topology Appl., 196, 229–240 (2015)
Jindal A., McCoy R. A., Kundu S.: The open-point and bi-point-open topologies on C(X). Topology Appl., 187, 62–74 (2015)
Kazimirz Kuratowski, Topology, Vol. I, Academic Press (New York–London, 1966).
Miller A. W.: Mapping a set of reals onto the reals. J. Symbolic Logic, 48, 575–584 (1983)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by Act 211 Government of the Russian Federation, contract 02.A03.21.0006.
Rights and permissions
About this article
Cite this article
Osipov, A.V. On separability of the functional space with the open-point and bi-point-open topologies. Acta Math. Hungar. 150, 167–175 (2016). https://doi.org/10.1007/s10474-016-0654-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-016-0654-6