Abstract
In this chapter, we study various topological properties of the uniform, fine and graph topologies on the space C(X, Y), the set of all continuous functions from a Tychonoff space X to a metric space Y. In particular, we study the metrizability, first countability and various completeness properties of the uniform, fine and graph topologies on C(X, Y).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 The Author(s)
About this chapter
Cite this chapter
McCoy, R.A., Kundu, S., Jindal, V. (2018). Metrizability and Completeness Properties of \(C_{\tau } (X, Y)\) for \(\tau = d,f, g\). In: Function Spaces with Uniform, Fine and Graph Topologies. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-77054-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-77054-3_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77053-6
Online ISBN: 978-3-319-77054-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)